Any description of the Fender Jazz Bass is neccessarily going to involve a lot of comparison the the Fender Precision Bass. They were, after all, the first two electric basses Leo Fender ever designed. A lot of people think he got it right the first time with them both and, judging by the amount of people who still use them more than 50 years later, he did.
Although the manufacturing process has changed dramatically since the '50s, and some "improvements" have been made, such as graphite-reinforced necks, the Jazz Basses being produced by Fender nowadays are much the same as the original. It still has narrow string spacing at the nut, the same comfortable offset body shape, and two single-coil pickups which act as a big humbucker when the volume for each is up. The fact that it has two pickups, each with their own volume control, means that the jazz bass can produce a bigger variety of sounds than the Precision. For this same reason, the Jazz has less of a "signature" sound than the precision, which makes it harder to pin down when listening to a bassline in the mix.
The Jazz is probably the most copied bass in the world. While companies that copy Precision Basses almost always make inferior rip-offs, there are quite a few boutique luthiers (most notable Sadowsky, who make almost nothing else) that make jazz copies costing significantly more than an original Fender one. I think this is a good thing. For me, the whole point of Fender instruments is that they are as simple as possible, and not simpler. Boutique jazzes generally have a lot of fancy stuff, like exotic wood veneers, expensive finishes, and a very good fit and finish, none of which makes any difference to the actual sound coming from the bass. Fender Jazzes still compete very well with basses costing threee times the price when it somes to tone.
Although they have lost their hold slightly since the 80's, Fender Jazz Basses are still probably the most popular instruments for professional session bassists. Jazz basses require very little work to make them sound good in the mix. This is a very important attribute since, in the studio, time is money. Producers will often insist on a Fender, or at least a Fender-style bass being played, since they know they can get a good sound out of it. It should be noted that I said "Fender", and not Jazz. Precision basses also sound very good in the mix, and share a LOT of the same good points as the jazz, but they're a bit less versatile, with only the one pickup. It's not uncommon for a session bassist, on pulling out his shiny new Warwick, to be asked "Where's your Fender?" before he even gets a chance to plug it in.
Famous Jazz Bass Players