I've got a favorite Les Paul, a favorite Strat, and a favorite korina, among others...
Amaterasu, a Guitar Trader pre-Historic. Hand carved and my favorite LP ever since I bought her new back in '83. Just feels perfect in my hands after all this time, super responsive and a lovely crisp & woody character to the tone. Very inspiring, really does behave like a vintage axe. Of course, she's older now than '59s were when I first got her... Just as with my #1 PRS, I think of her more as a collaborator than merely a tool.

Here's a pic that shows her top a little better- not insanely flamed like some recent ones, pretty similar to many of the original 'bursts though.
Lady Blue, my favorite Strat. Refretted and refinished before I got her, but she was born in October '63. Supernaturally vibrant and absolutely sweetest sounding of the 25 or so Strats I've owned over the years. At the time (1981) friends said it was crazy to pay nearly a thousand dollars for any Strat, even if it had been an original 50s one. But I knew from the very first couple of notes I played that she was something very special. Never regretted it for a single moment. Plenty of old guitars have mojo. Lady Blue has magic.
As for korina guitars, I've always had kind of a thing for those. Mine include an '82 Moderne, two korina Explorers, and a korina Firebird as well as an '07 korina/Brazilian McCarty. But probably my favorite is this McNaught doublecut. Maple top but the neck and body are very lively black korina and it plays amazingly well; David makes these with his extreme version of a long tenon neck joint that goes all the way to the bridge. Great natural sustain, fat sweet tone from the stock RioGrande humbuckers. Nice quilt too, though that isn't what made her a favorite.
Also have a few others I like just because they're oddballs, different from the run-of-the-mill Gibsons, Fenders and PRSs.