Are there any professional, gigging musicians who use someone else's signature guitar? Because I really don't know any...
Jari Maenpaa (sp?) from Wintersun uses a JEM and PGM live but i can't think of anyone else who uses someone elses signature guitar.
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matt tuck from BFMV uses randy rhoads
matt heafy from trivium used to use razorback

edit- the Gibson Les Paul is technically a signature model so loads of people do
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Sure, I've seen a guy on mtv using a Korn signature guitar a couple of years back, I don't remember the guy's name though.
Those who are not popular enough to get an own signature guitar will just stick to what they like best. Many get custom build gear though.

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the Gibson Les Paul is technically a signature model so loads of people do

Lots of people play razorbacks and rhoads.
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I know several people (Proffesionals) use ESP's Stephen Carpenter signatures, and I really can't blame them, either, a fan of Steph or not. They're nice.
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well frank iero from mcr uses a zakk wylde les paul on occasion.
This band isn't really big but I saw them last night they were called Fight! Fight Fight! and the guitarist used a Tom Delonge Strat. They had an endorsment from crate if that matters about credibility of anything.
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matt tuck from BFMV uses randy rhoads
matt heafy from trivium used to use razorback

edit- the Gibson Les Paul is technically a signature model so loads of people do

Padget also has a bunch of different signature guitars, Michael Amott's Ninja, for example.
John Mayer plays a modified Stevie Ray Vaughan signature Strat live. He switched out the gold hardware for chrome, changed the pickups (I believe), and changed the pickguard.
His signature model is basically an SRV signature with his modifications.
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Look at everyone who owns a Les Paul. There are also a lot of Ibanez JEM and Universe players (props to whoever said Jari Maenpaa), and those that play the Jackson Randy Rhoads model. I know there are a bunch of newer metal bands that use the ESP Steph Carpenter 7 string model (the guitarists in Suicide Silence use them, Devin Townsend [cheer] uses one, and a few more but i can't remember). I've seen a bunch of bands with the Dean Razorback and Razorback V, so I guess that's a signature model even though Dime never played one (or did he?).
the guy from Reliant K used a Tom Delonge signature Gibson. i cant think of anyone else right off the top of my head though.
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Can I just say, the Jackson RR series aren't signatures, the Gibson Les Paul series aren't signature guitars and neither are the Ibanez JEM/UV (aside from the JEM7VWH, otherwise it's just the line of guitars Steve Vai pretty much invented, he doesn't actually play any JEMs (or at least it's very rare to see him play any other jems) beside's his 7VWHs (or the floral FLO was that got turned white)).

But plenty of people have used other's signatures in the past, rarely as a main guitar though.