If there's anybody else here who would have thought of the choices I'm about to name, I'd be shocked to the point of insanity.
I'm a huge fan of Bonnie Pink, and a lot of her music has fantastic basslines. I'm sure plenty of us have had songs we skipped over or didn't pay much attention to until something just clicked one day. This is a classic example of this:
Hohoemi no Kate
I can't listen to this song all the way through, I always end up rewinding and playing it again somwhere just past halfway through. It pretty much takes a distraction to get me off it. Thanks to some help found here, I discovered that the bassist on this track is most likely Tore Johansson, the longtime producer of the Cardigans. I'm still trying to figure out how best to approach catching this tone.
And the other unusual source: the soundtrack for the Playstaton (yes, Playstation, not PS2 or PS3) fighting game, Street Fighter EX+a. SFEX was an arcade game originally, and for the PS1 port, they redid all the music with live instrumentation. The whole soundtrack has quality bass, but there are three songs which are most noteworthy to me:
Sakura Mankai
I don't really know what to say about this one, other than I love it.
Strange Sunset
I want this tone so badly. The smoothness, and the bite. Man. That' sabout the closest as I think I've heard to what I would call my ideal tone.
Under Tube
Another great bassline, full of tasty fretless mwah.