Fender's Jazz and Precision models are the most popular. The Precision is known for its solid, earthy tone, while the Jazz has more "sizzle" for funk and percussive playing.
My favourite bass...
The Fender Precision Bass and Jazz Bass. Other "standards" of the bass guitar world include the MusicMan Stingray, the Rickenbacker 4003 and to a lesser extent the Gibson EB-3.