For my money, on a mountain bike, it’s been the Shimano Deore LX. (It’s gotten some alright reviews, too.) Twelve years and still going strong on my full-suspension, even when practically everything else has needed replacement.
For my tri bike, I’ve got Shimano’s Dura-Ace 7800. Still, only about a year on that, but so far it’s been rock solid, seamless shifting.
As far as the best available at any price for a road bike, I’ve always heard it was Campagnalo. But I’d also like to hear anyone’s personal experience.