In my own biased opinion it is Israel Lopez (Cachao)
I’ll throw my 2 cents in. Cliff Burton was amazing on Metallica’s early albums…just incredible. I’m not sure if he’s under the 25 year limit, but I’m just putting the limit at 1980. Find ‘Anesthesia - Pulling Teeth’ if you can. To bad he’s not around anymore. 
A man gives his son an electric bass for his 15th birthday, along with a coupon for four bass lessons. When the son returns from his first lesson, the father asks, “So, what did you learn?” “Well, I learned the first five notes on the E string.” Next week, after the second lesson, the father again asks about the progress, and the son replies, “This time I learned the first five notes on the A string.” One week later, the son comes home far later than expected, smelling of cigarettes and beer. So the father asks: “Hey, what happened in today’s lesson?” “Dad, I’m sorry I couldn’t make it to my lesson; I had a gig!”
He may have been around years before, but he was virtually unknown until 1984 when Marty DiBergi’s This is Spinal Tap was released.
The greatest bass player of the last 25 years (and of all time) is Derek Smalls!
Well, since it was Geddy Lee who inspired me to pick up the bass almost 20 years ago, he is the standard by which I judge all other bassists.
So with that in mind, I would like to put in a vote for Rick White, the bassist & primary composer with the Seattle jazz trio Ecstasy In Numbers
Check them out here: http://www.ecstasyinnumbers.com
Hmmm. Dammit, the only sound clips are from their first album, with a different bass player. Oh well.
Paul D’Amour’s parents go to my church…
Another nod to Mike Watt.
Only bassist I’ve seen break a string in the middle of the show. The top string.
And I’ve seen him do it twice.
That doesn’t make him agreat bassist, but it speaks to the ferocity with which he plays.
I also saw him attempt to play with a monitor provided by the venue. Basically, it was a piece of crap and he couldn’t hear himself play, so after a few attempts at fixing it he just said “fuck it” and turned it off. He played the next hour with his eyes shut, just going by memory, gut and feel. And he blew me away.
If we’re keeping a tally, then chalk up another one for Watt.
Hooky
I saw Flea break a string. In the middle of the song. And it was his E string too. And he didn’t stop for a second. He played the entire rest of the show (about half of it) without that string. It was beautiful, man.
Robert Trujillo, now of Metallica but formerly of Infectious Grooves and Suicidal Tendecies. Check out the first couple IG Cds to hear why! 
Update:
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Claypool–6
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Watt and Hook–4
Everyone else is the same, with a few new additions with one vote.
NOTES: Mike Watt plays harder than anyone I have ever seen. I too saw him break a string, and he also pounded his bass into his rig so hard while basically humping it, that he tore some wood out of the headstock. I think I would rather see Watt live than any of the other guys, even though I don’t personally feel he is as talented as some of them. None of these other guys can match his energy. (Remember, I haven’t seen all of these guys, but I have seen most of them).
Trujillo is a guy I always forget about, but his stuff for Infectious Grooves “The Plague that makes your Booty Move” is incredible. Good call twit.
I guess to wrap it up, I will say first guy to 10 votes wins?
My vote goes for Fat Mike of NOFX. It’s just really good bass, and makes me wish I had never sold mine.