Gender is a concept that originally seemed to only exist with the Nidorans but then expanded in Gold & Silver to be a fairly large dynamic in the games. Almost every Pokémon has a specific gender ratio and the ratio determines how likely it is that you'll get a male Pokémon or a female Pokémon. Some Pokémon have a simple 50/50 ratio while others have a 75/25 and even some as low as 87.5/12.5. Some Pokémon have various differences in appearance based upon their gender
There is only one case of a Pokémon having a different gender ratio as its evolution. Azurill has a 25/75 ratio while Marill has a 50/50 one meaning that one third of female Azurills may change gender to male upon evolution.
In addition to that, there are certain Pokémon which are only male or only female. These are listed below.

Male Only Pokémon
Nidoran♂ Poison Point Rivalry Hustle	Nidorino Poison Point Rivalry Hustle	Nidoking Poison Point Rivalry Sheer Force	Hitmonlee Limber Reckless Unburden	Hitmonchan Keen Eye Iron Fist Inner Focus
Tauros Intimidate Anger Point Sheer Force	Tyrogue Guts Steadfast Vital Spirit	Hitmontop Intimidate Technician Steadfast	Volbeat Illuminate Swarm Prankster	Latios Levitate
Mothim Swarm Tinted Lens	Gallade Steadfast Justified	Throh Guts Inner Focus Mold Breaker	Sawk Sturdy Inner Focus Mold Breaker	Rufflet Keen Eye Sheer Force Hustle
Braviary Keen Eye Sheer Force Defiant	Tornadus Prankster Defiant	Thundurus Prankster Defiant	Landorus Sand Force Sheer Force

Female Only Pokémon
Nidoran♀ Poison Point Rivalry Hustle	Nidorina Poison Point Rivalry Hustle	Nidoqueen Poison Point Rivalry Sheer Force	Chansey Natural Cure Serene Grace Healer	Kangaskhan Early Bird Scrappy Inner Focus
Jynx Oblivious Forewarn Dry Skin	Smoochum Oblivious Forewarn Hydration	Miltank Thick Fat Scrappy Sap Sipper	Blissey Natural Cure Serene Grace Healer	Illumise Oblivious Tinted Lens Prankster
Latias Levitate	Wormadam Anticipation Overcoat	Vespiquen Pressure Unnerve	Happiny Natural Cure Serene Grace Friend Guard	Froslass Snow Cloak Cursed Body
Cresselia Levitate	Petilil Chlorophyll Own Tempo Leaf Guard	Lilligant Chlorophyll Own Tempo Leaf Guard	Vullaby Big Pecks Overcoat Weak Armor	Mandibuzz Big Pecks Overcoat Weak Armor
Flabébé Flower Veil Symbiosis	Floette Flower Veil Symbiosis	Florges Flower Veil Symbiosis	Salazzle Corrosion Oblivious	Bounsweet Leaf Guard Oblivious Sweet Veil
Steenee Leaf Guard Oblivious Sweet Veil	Tsareena Leaf Guard Queenly Majesty Sweet Veil

Gender-Based Evolution

Since Generation IV, there have been a few Pokémon who evolved based upon their gender. Sometimes the genders provide an alternate evolution while on others, such as Combee, the Pokémon will only evolve if it is a female..

Pic	Name	Base Stats & Type						Evolution Method	Evo Pic	Evo Name	Evo Base Stats & Type
		HP	Att	Def	S.Att	S.Def	Spd				HP	Att	Def	S.Att	S.Def	Spd
	#412 Burmy							Level 20 ♂ Only		#414 Mothim
		40	29	45	29	45	36				70	94	50	94	50	66
	#281 Kirlia							Dawn Stone ♂ Only		#475 Gallade
		38	35	35	65	55	50				68	125	65	65	115	80
	#412 Burmy							Level 20 ♀ Only		#413 Wormadam
		40	29	45	29	45	36				60	59	85	79	105	36
	#415 Combee							Level 21 ♀ Only		#416 Vespiquen
		30	30	42	30	42	70				70	80	102	80	102	40
	#361 Snorunt							Dawn Stone ♀ Only		#478 Froslass
		50	50	50	50	50	50				70	80	70	80	70	110
	#757 Salandit							Level 33 ♀ Only		#758 Salazzle
		48	44	40	71	40	77				68	64	60	111	60	117

Breeding Pokémon

The more commonly used feature of genders is the Breeding feature. This feature has you put a male and a female Pokémon into the day care centre and breed to get the base form of the female Pokémon. The male parents are the ones used to transfer moves to the Pokémon. For further information, check the Breeding section.

Finding & Capturing Pokémon

Previously, gender didn't play a part in the capturing of Pokémon. However, there are a few elements which will allow you to manipulate the wild Pokémon of which you will encounter and even increase the chance of capture of the Pokémon.
First, if the Pokémon at the head of your party has the Cute Charm ability, there is a 66% higher chance of you encountering a Pokémon of the opposite gender to your front Pokémon.
Second, in HeartGold & SoulSilver, you have the ability to get the item; the Love Ball. This ball increases the chances of capturing a Pokémon of the opposite gender to your active Pokémon by a factor of 8 making the capture calculation;
    CatchValue = ((( 3 * Max HP - 2 * HP ) * ((Catch Rate * 8) * 1 ) / (3 * Max HP) ) * Status Modifier

Attract Status

The Attract status is the main use of genders you shall see in battle. This status is a hidden status like Confusion. It requires the opponent to be of the opposite gender as the user and the user to have a gender

Effects:
The Pokémon afflicted cannot attack 50% of the time

Immunities:
Pokémon with the Oblivious ability
Pokémon of the same gender as the user
Genderless Pokémon (unless used by Mew or Cryogonal)

Methods of Healing
Using the attacks Heal Bell or Aromatherapy
Using the specialised items that follow:

Picture	Name	Effect
	Mental Herb	Removes Infatuation status; can only be used once
	Red Flute	Heals from Infatuation

Methods of Inflicting
If you or the opponent has the Cute Charm ability and the Pokémon attacking that Pokémon makes physical contact, then there is a 30% chance of the attacker being Infatuated
Using the following attacks:

Name	Type	Cat.	Chance	PP	Att.	Acc.	Effect
Attract			100%	15	--	100	Makes the opposite gender less likely to attack.

Moves Affected by Gender

There are a few moves that are affected by gender. These moves require the opponent to be of the opposite gender before their effect is implemented. There are currently no attacks which only affect the Pokémon of the same gender of the user.

Name	Type	Cat.	Chance	PP	Att.	Acc.	Effect
Attract			100%	15	--	100	Makes the opposite gender less likely to attack.
Captivate			100%	20	--	100	If it is the opposite gender of the user, the target is charmed into harshly lowering its Sp. Atk stat.

Abilities Affected by Gender

In addition to the various moves, there are numberous abilities.

Genderless Pokémon

Finally, there are a few dozen Pokémon who are immune to all of these effects and are in fact devoid of Gender, some still breedable with Ditto but others not being breedable. That said, Mew and Cryogonal both learn Attract which will infatuate other Genderless Pokémon

Genderless Pokémon
Magnemite Magnet Pull Sturdy Analytic	Magneton Magnet Pull Sturdy Analytic	Voltorb Soundproof Static Aftermath	Electrode Soundproof Static Aftermath	Staryu Illuminate Natural Cure Analytic
Starmie Illuminate Natural Cure Analytic	Ditto Limber Imposter	Porygon Trace Download Analytic	Articuno Pressure Snow Cloak	Zapdos Pressure Static
Moltres Pressure Flame Body	Mewtwo Pressure Unnerve	Mew Synchronize	Unown Levitate	Porygon2 Trace Download Analytic
Raikou Pressure Inner Focus	Entei Pressure Inner Focus	Suicune Pressure Inner Focus	Lugia Pressure Multiscale	Ho-Oh Pressure Regenerator
Celebi Natural Cure	Shedinja Wonder Guard	Lunatone Levitate	Solrock Levitate	Baltoy Levitate
Claydol Levitate	Beldum Clear Body Light Metal	Metang Clear Body Light Metal	Metagross Clear Body Light Metal	Regirock Clear Body Sturdy
Regice Clear Body Ice Body	Registeel Clear Body Light Metal	Kyogre Drizzle	Groudon Drought	Rayquaza Air Lock
Jirachi Serene Grace	Deoxys Pressure	Bronzor Levitate Heatproof Heavy Metal	Bronzong Levitate Heatproof Heavy Metal	Magnezone Magnet Pull Sturdy Analytic
Porygon-Z Adaptability Download Analytic	Rotom Levitate	Uxie Levitate	Mesprit Levitate	Azelf Levitate
Dialga Pressure Telepathy	Palkia Pressure Telepathy	Regigigas Slow Start	Giratina Pressure Telepathy	Phione Hydration
Manaphy Hydration	Darkrai Bad Dreams	Shaymin Natural Cure	Arceus Multitype	Victini Victory Star
Klink Plus Minus Clear Body	Klang Plus Minus Clear Body	Klinklang Plus Minus Clear Body	Cryogonal Levitate	Golett Iron Fist Klutz No Guard
Golurk Iron Fist Klutz No Guard	Cobalion Justified	Terrakion Justified	Virizion Justified	Reshiram Turboblaze
Zekrom Teravolt	Kyurem Pressure	Keldeo Justified	Meloetta Serene Grace	Genesect Download
Carbink Clear Body Sturdy	Xerneas Fairy Aura	Yveltal Dark Aura	Zygarde Aura Break	Diancie Clear Body
Hoopa Magician	Volcanion Water Absorb	Type: Null Battle Armor	Silvally RKS System	Minior Shields Down
Dhelmise Steelworker	Tapu Koko Electric Surge Telepathy	Tapu Lele Psychic Surge Telepathy	Tapu Bulu Grassy Surge Telepathy	Tapu Fini Misty Surge Telepathy
Cosmog Unaware	Cosmoem Sturdy	Solgaleo Full Metal Body	Lunala Shadow Shield	Nihilego Beast Boost
Buzzwole Beast Boost	Pheromosa Beast Boost	Xurkitree Beast Boost	Celesteela Beast Boost	Kartana Beast Boost
Guzzlord Beast Boost	Necrozma Prism Armor	Magearna Soul-Heart	Marshadow Technician	Poipole Beast Boost
Naganadel Beast Boost	Stakataka Beast Boost	Blacephalon Beast Boost	Poipole Volt Absorb

Gender Differences

Since Generation IV, there have been a few Pokémon who have different appearances based on their gender. These differences are set in stone and cannot be altered. These propogate across both the main series games and spin-off series games such as Pokémon GO.

No.	Male	Female	Name	Description
#003			Venusaur	Female Venusaur's Flower has a Seed in it
#012			Butterfree	Butterfree's Wing Pattern is different
#019			Rattata	Female Rattata's Whiskers are Smaller
#020			Raticate	Female Raticate's Whiskers are Smaller
#025			Pikachu	Female Pikachu's Tail has a groove in it
#026			Raichu	Female Raichu's Tail lacks the point at the end
#041			Zubat	Female Zubat's teeth are smaller
#042			Golbat	Female Golbat's teeth are smaller
#044			Gloom	Female Gloom has a different flower pattern
#045			Vileplume	Female Vileplume has a different flower pattern
#064			Kadabra	Female Kadabra has a smaller moustache
#065			Alakazam	Female Alakazam has a smaller moustache
#084			Doduo	Female Doduo have beige necks. Male Doduo have black necks
#085			Dodrio	Female Dodrio have beige necks. Male Dodrio have black necks
#097			Hypno	Male Hypno has a smaller collar
#111			Rhyhorn	Female Rhyhorn has a smaller horn
#112			Rhydon	Female Rhydon has a smaller horn
#118			Goldeen	Female Goldeen has a smaller horn
#119			Seaking	Female Seaking has a smaller horn
#123			Scyther	Female Scyther has a bigger abdomen
#129			Magikarp	Female Magikarp has white whiskers
#130			Gyarados	Female Gyarados has white whiskers
#154			Meganium	Female Meganium has smaller antennae
#165			Ledyba	Female Ledyba has smaller antennae
#166			Ledian	Female Ledian has smaller antennae
#178			Xatu	Female Xatu has less stripes on her body
#185			Sudowoodo	Female Sudowoodo has smaller antennae
#186			Politoed	Female Politoed has smaller spots on their cheek
#190			Aipom	Female Aipom has longer hair
#194			Wooper	Female Wooper have less bars on their antennae
#195			Quagsire	Female Quagsire have smaller back-fins
#198			Murkrow	Female Murkrow has a smaller 'hat'
#202			Wobbuffet	Female Wobbufet appear to wear lipstick
#203			Girafarig	Female Girafarig have a bigger yellow pattern on their body
#207			Gligar	Male Gligar have a bigger stinger
#208			Steelix	Male Steelix have extra teeth
#212			Scizor	Female Scizor have a bigger abdomen
#214			Heracross	Female Heracross' horns are shaped similar to hearts
#215			Sneasel	Female Sneasel have smaller head feathers
#217			Ursaring	Male Ursaring's have longer shoulder hair
#221			Piloswine	Female Piloswine have smaller tusks
#224			Octillery	Female Octiller have smaller yellow bumps & feelers
#229			Houndoom	Female Houndoom have smaller horns
#232			Donphan	Female Donphan have smaller tusks
#255			Torchic	Female Torchic have a small speck on their rear
#256			Combusken	Female Combusken have smaller head feathers
#257			Blaziken	Female Blaziken have smaller head feathers
#267			Beautifly	The red spot on Female Beautifly is smaller
#269			Dustox	Female Dustox have smaller antennae
#272			Ludicolo	Female Ludicolo's Body Stripes are thinner
#274			Nuzleaf	Female Nuzleaf have smaller head leaves
#275			Shiftry	Female Shiftry have smaller hand-leaves
#307			Meditite	Female Meditite's ears are lower on their head
#308			Medicham	The top of Female Medicham's head is smaller
#315			Roselia	Female Roselia have bigger body leaves
#316			Gulpin	Female Gulpin have smaller head feathers
#317			Swalot	Female Swalot have smaller whiskers
#322			Numel	Female Numel have bigger humps
#323			Camerupt	Female Camerupt have bigger Volcanic Humps
#332			Cacturne	Female Cacturne has a giant diamond on their body
#350			Milotic	Female Miltoic have larger eyebrows
#369			Relicanth	Female Relicanth have smaller jaws
#396			Starly	Male Starly have larger foreheads
#397			Staravia	Male Staravia have larger foreheads
#398			Staraptor	Male Staraptor have larger foreheads
#399			Bidoof	Male Bidoof have extra lumps to their tails
#400			Bibarel	Male Bibarel have bigger faces
#401			Kricketot	Female Kricketot have larger collars
#402			Kricketune	Female Kricketune have smaller moustaches
#403			Shinx	Female Shinx have shorter head hair
#404			Luxio	Female Luxio have shorter head hair
#405			Luxray	Female Luxray have shorter head hair
#407			Roserade	Female Roserade have larger capes
#415			Combee	Female Combee have a Red spot on the bottom face's forehead
#417			Pachirisu	Male Pachirisu's forehead pattern is longer
#418			Buizel	Male Buizel have two stripes on their back. Female Buizel only have one.
#419			Floatzel	Male Floatzel have two stripes on their back. Female Floatzel only have one.
#424			Ambipom	Female Ambipom have longer head hair
#443			Gible	Male Gible have a groove in their fin
#444			Gabite	Male Gabite have a groove in their fin
#445			Garchomp	Male Garchomp have a groove in their fin
#449			Hippopotas	Male & Female Hippoptas have their colour scheme switched
#450			Hippowdon	Male Hippowdon are brown. Female Hippowdon are Grey
#453			Croagunk	Female Croagunk's have smaller chests
#454			Toxicroak	Male Toxicroak have larger chins
#456			Finneon	Female Finneon have larger tails
#457			Lumineon	Female Lumineon have larger fins
#459			Snover	Female Snover's trunks are more snow covered
#460			Abomasnow	Female Abomasnow have larger breast hair
#461			Weavile	Male Weavile have larger ear feathers
#464			Rhyperior	Female Rhyperior have smaller horns
#465			Tangrowth	Female Tangrowth have larger hands
#473			Mamoswine	Male Mamoswine have larger tusks
#521			Unfezant	Male Unfezant have a mask on and have a greenish tinge to their feathers while female Unfezant lack the mask and are more brown.
#592			Frillish	Male Frillish are blue while female are pink. Female's tips on tentacles are more curved.
#593			Jellicent	Male Jellicent are blue while female are pink. Male's collar lare thicker, covering the mouth while female's are smaller
#668			Pyroar	Male Pyroar have a full mane that looks like the kanji symbol for fire (大) while female Pyroar have a smaller mane
#678			Meowstic	Male Meowstic is blue while female is white. Male Meowstic get more Status moves while Female Meowstic are more focused on attacking. They have different Hidden Abilities