Usually, I go for the characters that have a balance of speed and strength, yet have a somewhat unconventional fighting style. Although sometimes I'll go for the slower, defensive types.
Street Fighter: Sagat, or as I like to call him, Captain Tiger. TIGER SHOT! TIGER UPPERCUT! TIGER KNEE! TIGER RAID! TIGER GENOCIDE! Other favourites: Ryu, M.Bison, Fei Long
Soul Calibur: Cervantes - His swords have a short range, but his moves more than make up for it, especially his Psycho Crusher-style attack. Other favourites: Siegfried, Raphael, Sophitia
Smash Bros: Captain Falcon - His mobility makes up for his slow attacks, and a well-placed Falcon Knee is almost as satisfying to land as Akuma's Raging Demon.
Other favourites: Fox, Donkey Kong, Ganondorf
Mortal Kombat: Sub Zero - Freezing people is awesome, especially if it's done with an Ice Clone (MK3) to punish them for jumping at you. Other favourites: Liu Kang, Shao Kahn