The criteria a bass must meet in order to qualify as a "bass with balls" are simple: it must be able to cut through the ungodly racket made by the average guitarist playing with distortion, and it must have a distinct tone that is instantly recognizable as belonging to it and no other bass. Incidentally, any of the 4 basses on the list could bludgeon a 300 pound Hell's Angel into a coma and then play a 2 hour set. This doesn't count toward their Bass with Balls ranking, but it's nice to know that classic style, rugged construction, and great sound seem to converge in the world's greatest rock basses.
(I regret the sexist connotations of "balls," but I'm afraid there's really no equivalent politically correct metaphor. If it's any consolation to feminists, a person's body doesn't need to have balls in order for them to play music that does. For example, Janice Joplin, Heart and Blondie have a surfeit of balls, while George Michael and James Blunt have no balls whatsoever. But I digress.)
introduced by Leo Fender in 1951, the Fender Precision Bass, nicknamed the "P-bass" was the very first mass produced electric bass guitar. Its pickup configuration, which consists of one split single coil, and its body shape, which looks like a Fender Stratocaster's heavyset, dowdy sister, have been imitated by about 85% of introductory (i.e. cheap) model basses in the last 55 years.
A real Fender P-bass, when strung with new stainless steel strings of a decent gauge and played through a good amp, will yield a full, warm, snarling, crisp, woody, slightly nasal tone that is excellent for rock and punk but only passable for metal (Ozzy can get away with it, Pantera probably couldn't). With older or nickel strings, poorly EQ'd or played through a bad amp, it can become mushy, bland, inobtrusive and pedestrian, like the bass you can't remember from every McDonald's commercial you've ever seen. Unfortunately, the Fender brand name attracts more enthusiasts than it does actual musicians, and about half of the yahoos playing one don't realize that there's a real art to getting it to sound good.
For those who would like to listen to what a P-Bass sounds like when things go right, I suggest listening to Ozzy Osbourne's "I Just Want You" through headphones (while watching the video--it's great). And In celebration of music with balls, here's Heart's "Barracuda."