Depends on what I'm doing with it.
For carry-defense my favorite caliber is .45acp, though right now I'm hauling around either a 9mm, or a .380.
For home defense I like a 12 gauge.
For all around general, one-size-fits-none, I would carry a .45LC. Not the ideal caliber for all jobs, but IMNSHO the most versatile caliber I can get in a pistol cartridge.
For just plinking, .22 is the best and cheapest way to go. You can shoot all day without breaking the bank, or getting fatigued.
Favorite large rifle caliber is another toss up. I like the 7mm magnum because I like the power and flat trajectory of the round. However, my brother has a Remmington Rolling Block that he bought chambered in .45spanish for twenty five bucks back in the sixties. It was an antique military rifle. He had it rechambered to 45/70 and sporterized. I've been trying to get him to part with that Rolling Block for years: I love that rifle.
I also like .38special, 357magnum, .41magnum, .44special and magnum, and I even liked that monster Casull I fired today (although my wrist is still a bit tender from those 335 grain slugs. I much preferred firing the 230 grain half jacket hollow points.), and I even like my friend's .50 mag DE (though firing the thing on an enclosed range gave me a nose bleed).
Personally I love to shoot and will fire just about anything I can get my hands on, including bb guns and pellet rifles. If someone offers to let me shoot some new exotic caliber that I've never fired before I'm all for it. Therefore, my favorite caliber is the one in my hand.