Along with Fire and Grass, Water Pokémon are one of your options for your very first Pokémon in most of the games. Water moves are powerful, deal a lot of damage, and will make short work of Fire, Ground, and Rock-type Pokémon.
I heard that Mudkips are pretty popular. Squishy and adorable, Mudkip also has a killer evolution chain: Swampert is awesome, and being Water/Ground type eliminates Water's weakness to Electric attacks.
Gyarados is the awesome, feared dragon that evolves from the lowly Magikarp. Magikarp is famous for being the lamest of all Pokémon, since all it can do is flop around helplessly. Just get it up to level 20 and see what havoc you can wreck.
One of the original three Eevee evolutions (along with Jolteon and Flareon) Vaporeon is, let's face it, still the best choice for your Eevee. Make sure to get a Water Stone!
The adorable baby manta ray, Mantyke evolves into Mantine when you level it up with a Remoraid also in your party. Mantyke is, at the time of this writing, the only Pokémon who evolves in this unique fashion.
The Loch-Ness Monster of Pokémon, the combination Water/Ice type Lapras is often shown in the anime as a Pokémon that ferries humans and other Pokémon.
select one here...