In addition to new evolutions to old Pokemon, pre-evolutions were also introduced in Gold and Silver. These Pokemon are known as baby Pokemon, and most can only be acquired through hatching an egg. Many of them evolve via happiness and learn moves that involve their cute charm that their later evolutions can't learn. These Pokemon cannot breed.
How is a baby formed?
To get a baby Pokemon, you must put two Pokemon of opposite genders together in the Day Care. As long as they fit in the same egg groups, aren't legendary, or involves Ditto, you will get an egg. The offspring will be the lowest form of the mother's species. For some Pokemon this results in a baby Pokemon. Check the Pokedex for what Pokemon are in what egg group. Click here for details
Pichu, the adorable Electric-type baby mouse Pokemon, is the first in the trio of Kanto babies that evolve via happiness. Pichu gets Charm and Sweet Kiss, which are kind of useless on a Raichu.
The star shaped Cleffa is the second of this trio. It has the Normal-typing and learns Encore in addition to Sweet Kiss and Charm. Clefable is very versatile in battle so try using it if you get it in Crystal.
Igglybuff, the last Kanto baby that evolves via happiness, is a Normal-type with high HP. It has frail defenses though so avoid using it in battle. It too gets Sweet Kiss and Charm.
With a mother unique to Generation II, Togepi is the only baby Pokemon that has no relatives in Generation I. It's a Normal-type like Igglybuff and Cleffa, but evolves into a Normal/Flying-type when it has high happiness. Togetic is somewhat versatile and makes a great Fly user.
Tyrogue, unlike the other baby Pokemon, is a Fighting-type given to the player at Level 10 in Mt. Mortar. He can evolve into any of the three Hitmons at Level 20 using a convoluted system: if Attack is higher than Defense, you'll get Hitmonlee, if Defense is higher than Attack, you'll get Hitmonchan, if both are equal, you'll get Hitmontop. You have to breed any of those three with Ditto to get more Tyrogue.
The Psychic/Ice-type baby Pokemon Smoochum evolves at Level 30 into Jynx. It gets Sweet Kiss instead of Lovely Kiss which is arguably less useful on Jynx.
The Electric-type Elekid is a fine Mystery Egg alternative to Pichu in Crystal, with its mother only becoming available in Kanto. Elekid can get all three of the elemental punches unlike Smoochum and Magmar, giving it great coverage. It also evolves at Level 30.
Magby, the only Fire-type baby Pokemon to date, is available as soon as you get to Ecruteak City, though you can just use underleveled Magmar if you prefer. It learns Thunderpunch via TM to take out those pesky Water-types.