I have been thinking about this a lot since my band has been going through bass players like water(sound familiar Smoggy?).Now I am about to purchase a bass and become my own bass player for recording purposes anyway.
 But besides myself, I think the ultimate bass player for my playing and whom I'd love to lock in with would be.............
Doug Pinnick of Kings X. He has such a heavy groove and I love the tones he gets out of his rig. I think his playing might best suit my playing style.....ahhh...if only.

Of course, the Rush geek in me would also love to play with Geddy Lee, but overall my style probably would not fit in the long run. It's fun to dream and think of stuff like this though.

About ten come to mind, but I gotta go with Tony Levin.

Of course, this is subject to revision if Uma Thurman takes up the bass.  

lately, jeff berlin is my guy. but i like tony levin, too. he's just a cool dude all-around, in addition to being a great player.

jaco, also, if i wanted to torture myself, and he was available.

also always loved chris squire. everyone disses him for the rickenbacker, but i thought he had a great sound.

it's funny, cheffy. i was trolling for band sitches on craigslist or wherever, and in addition to finding some people to play with, i also befriended a sorta beginning chick bassist. we're supposed to hook up in january to fart around. i'm not sure if she's any good, but i thought it would be cool to try.

so i feel ya, but also encourage you to keep looking. something's gotta turn up. even if you have to prop them up somewhere.

This is hardâ€"I like so many.  As far as electric bass, Carol Kaye would be my current choice; she's a no-nonsense player who gets a good sound, and has good time.  

I don't really know many string bassists to offer an informed opinion.

EDIT:  I'd like to second Leland Sklar.

Paul McCartney or Rick Danko (if he were still with us)

oh, dont get me started on ms. kaye...  

and yea, there's a reason why leland is the first of the first callers.

session -> anthony jackson & pino palladino

anthony's the godfather of modern electric bass, and there's not one song from the '70s or '80s he didnt work on (the apprentice, anyone?).  he's a living legend.  and pino is easily his rightful heir.  the scotsman'll do a cheesy paul young song, and turn it into a masterpiece.  OR, he'll go on and define modern day r&b feels w/ jill scott, d'angelo, or erykah badu.  or he'll carry on john entwhistle's torch and rock out w/ the Who.  but it'll be hard to forgive his john mayer trio stint.  

rock -> jeff ament (pj) & rob deleo (stp)

both gents really know how to move a groove feel heavy, and yet not make it feel plodding.  they dance around the rhythm to keep it interesting yet hold it down.  i'd say 85% of my rock playing at one point or other were literally driven by their ideas/feels.

jazz -> ray brown & ron carter

they can both hold it down like a solid gold anchor and yet, swing like a bunch of motherpluckers.  their mark on jazz is incalculable.

fusion -> john patitucci & matt garrison

john's a bassist's bassist.  impeccable groove and time, who can move from upright to electric like he was changing pants.  matt's like a bolt of a tornado ready to lay havoc.

gospel -> Andrew Gouche & Maurice Fitzgerald

andrew's a producer as well, and knows a song from the inside out.  maurice needs to be locked up cause his grooves will kill.

any of these guys would be a HOOT.

Eddie Gomez

Jaco

Mel Schacher (I was always a big Grand Funk fan!)

I would say Geddy Lee and Sting. If you've played with Sting, it pretty much means you are a top notch drummer (following Copeland, Hakim, Katche, Colauita, Freese, etc, etc).

As for the John Mayer trio comment (Joker), I have actually enjoyed that cd! Especially with Steve Jordan laying down the groove back there.

Ditto, dude.  For the first time I found myself actually digging John Mayer due to this trio!