Battle Moveset

A Good Moveset for Latias would have to be this:

Attacks:

Dragon Claw/Psychic
Calm Mind
Recover
Thunderbolt/Ice Beam/Surf

Items Attached:

Leftovers OR
Soul Dew

Preferred Nature:

Bold

Strategy Using Latias

Soul Dew or not, this Pokémon is Uber. You may argue the point of its base stats, but when taking into account its type combo, move pool and trait, it is undeniably deserving of being in the same category as Rayquaza, Mewtwo and the like.

This set is your basic Special Tank. With 300+ Defence and only two physical weakness (one being to a type that struggles to gain STAB due to lacking of numbers and good attack base stats) it should be able to take physical hits pretty solidly. As far as Ubers are concerned, watch out for the likes of Sword Dance Groudon (with Hidden Power *Bug or Ghost*) and Choice Band Deoxys. You should also keep an eye out for Lugia, who can out-Calm Mind you and then PHaze you away with Whirl-Wind.

Since Soul Dew boosts Special Attack, you should be sorted for Special offence without the aid of Calm Mind, meaning this thing can launch offence the moment it comes into play. Your choice of moves is optional:

-Dragon Claw is nice since only one type resists it, a type which happens to have the misfortune of having low Special Defence in most cases.
-In Uber play, Psychic suffers, since the majority of Ubers are Psychic types (and there go resistant). However, Psychic hits Super-Effective on Heracross, one of the few non-Uber Pokémon that'll dent Latias.
-Ice Beam shouldn't be used in conjuncture with Dragon Claw since you waste type coverage, however the 4x effective on Rayquaza is undeniably handy.
-Thunderbolt and Surf team better with Dragon Claw for all-type coverage. Surf is handy since on a Kyogre based team you get a STAB-like boost while Thunderbolt can hurt the likes of Kyogre and Lugia.

Thunder also has the option of replacing Thunderbolt due to Kyogre use. To some extent, Solarbeam and HP Fire could be considered options as well, assuming you use Groudon on your team, though neither of these show any true advantage over any of the other moves Latias has access to.

You could also go for a more tank-like approach and rather than have a secondary offence, use Safeguard, Refresh or Substitute in your last move slot, allowing you to block potential status ailments. Roar is also an option if you lack a PHazer and fear certain Pokémon, however you'll see the most benefit from this if you use a Spiker on your team. Unfortunately, a lot of Ubers resist Spikes so you won't see much gain from it.

EV Corner:

EVs: 12 HP / 252 Def / 204 Spd / 42 SAtk or SDef Bold Nature (+Def, -Atk) @Leftovers

You need at least 307 Speed, to outrun Jolly Groudons and co. More speed could be added to outrun other Pokémon that you fear. Max Defence will buffer any physical hits Latias is forced to take, and combined with Recover, it should be able to out last the opponent. Excess EVs have been chosen to even out HP for Leftover recovery. It's up to you whether you wish to put the excess EVs into Special Attack or Special Defence.

EVs: 252 Def / 204 Spd / 54 SDef Bold Nature (+Def, -Atk) @Soul Dew

This set follows the same logic as above. It outruns Jolly Groudon and Timid Kyogre, it buffers physical attacks nicely, however this set doesn't have EVs designed for Leftovers and due to Soul Dew boosting Special Attack, the excess EVs are thrown in Special Defence.

Other Optional Sets: Latias@Soul Dew
Dragon Claw/Psychic
Recover
Ice Beam/Solarbeam
Thunderbolt/Thunder

The Latias that doesn't waste time Calm Minding. Switch in, decimate opposing Pokémon, switch out, Recover when necessary. Select a STAB move (I suggest Dragon Claw but when using Ice Beam, Psychic makes a friendlier choice) and then some backup moves. Thunder could be used to get opposing Kyogre's (and work with your own Kyogre's Rain Dance) and Solarbeam could be used to get opposing Groudon's (and work with your own Groudon's Sunny Day).

Latias@Leftovers
Dragon Claw
Wish
Protect/Safeguard/Refresh
Thunder Wave/Toxic

Wish-passing Latias. Protect works with Wish as an imitation Recover and it could work with Toxic. Refresh and Safeguard help against status ailments. Dragon Claw is just so you don't lack offence.

Latias@Leftovers
Reflect
Light Screen
Wish
Dragon Claw

Your basic Wish Passer + Reflect and Light Screen boosts. Also works nicely for 2v2 battles however it doesn't live up to Latias's potential.

Latias@Soul Dew
Psych up/Helping Hand
Psychic/Dragon Claw
Recover
Thunderbolt/Surf/Ice Beam

Basically a 2v2 Latias that Psych Ups a partners stat-ups or gives it a "Helping Hand".

Latias@Choice Band
Earthquake
Shadow Ball
Thunderbolt
Hidden Power [Bug or Rock]

A novelty at best but the surprise factor could actually get you a battle changing KO. Hidden Power [Bug] dents the likes of Celebi while Hidden Power [Rock] works with EQ for type coverage. Latios does this better unfortunately.

Strategy Against Latias

-Sticking a Special Wall in its way helps. Something like Snorlax who can match Calm Minds with Curses would be favourable, especially since Snorlax has Shadow Ball access, which will cut apart Latias pretty easily. Blissey can temporarily halt it but non-Toxic Blissey suffers from inability to do damage. Recover cancels out Seismic Toss and after 6 Calm Minds, Blissey will begin to run out of Softboileds to repel Dragon Claw/Psychic offence. Deoxys [Leaf] is also an option, though much like Blissey, it can suffer from its inability to do effective damage without the aid of Toxic.
-Lugia makes for a nice solution, since it has Whirlwind to rid itself of Latias problems, Pressure to drain Latias's PP and Calm Mind to stall it.
-Opposing Lati@s's using the Calm Mind strategy will halt it to some extent, though giving Latias one free turn to Calm Mind will make a difference.
-A handful of Choice Banders can cause Latias problems (Choice Band Seaking in a Kyogre team "hint hint".). -Metagross (with its resistance to both Latias's STABs and only Special weakness lying in a type that Latias can't access without the aid of Hidden Power) will be able to hurt it.

Fast Taunts, Toxic, Snatch and other "anti-stall" moves will interfere with the Calm Mind Latias. Tyranitar's Sandstorm can force Latias to recover more often since the majority don't have Leftovers to cancel out the negative effects of Sandstorm.

Contest Moveset

A good Contest Moveset for Latias would have to be this for the Cool Contest best with Lonely, Adament, Naughty or Brave Nature:

Attacks:

Calm mind
Psychic
Aerial Ace
Hyper beam

Items Attached:

Red Scarf

Strategy Using Latias

If you do the attacks in this following order you should have very few problems; 1st - Aerial ace, 2nd - Calm mind, 3rd - Psychic, 4th - Aerial Ace, 5th - Hyper beam

Locations in Games

Ruby/Sapphire/Emerald Random Grass & Waters in Hoenn after beating Elite Four (Sapphire/Emerald) Southern Island (Ruby/Emerald) Colosseum Trade from R/S/E Fire Red/Leaf Green Trade from R/S/E

Animé Appearences

Latios has had a single Animé Appearence. In it, it was in Alto Mare and and had to try and rescue her brother, Latios from Annie & Oakley Movie 5: Heroes - Latios & Latias