1) Chandler -- Matthew Perry had the best comic delivery of all the six actors, and the writers at first took advantage of this to give him all the best lines for the first few years. His inflections became too familiar after a while, so he asked the writers to change up how he spoken (and especially to get rid of his much parodied "Could it be any more ---?" formulation, which grew tiresome). but he was the most talented at comedy of the six actors, and was usually the funniest.
2) Monica -- The character was too often written to be just pretty and adorable, and when she was (such as when she was being cutsey with her older boyfriend Richard), Monica could be tedious. But I have to admit the hardest I ever laughed at the show was when the writers emphasized Monica's two funniest qualities--her OCD (particularly when it came to cleanliness) and, most of all, her competitiveness. "The One with the Frozen Embryos," where the six they play the stupid trivia game about one another, is the funniest of all the episodes to me, and it's because Courtney Cox's timing with regards to Monica's competitive streak is just insanely brilliant in this episode.
3) Phoebe -- In many ways she was the worst written of all the characters, and episodes with her character's family were usually trying. But Lisa Kurdrow is so naturally funny and has such brilliant unexpected timing that she made the character often hilarious.
4) Joey -- At first the character wasn't that funny, but the writers discovered how good Matt LeBlanc was at playing stupid and wrote the character to take advantage of that. The problem was that Joey wasn't very three-dimensional beyond that.
5) Rachel-- The character was written to be cute and adorable rather than smart, and of the six Jennifer Aniston has the most natural charisma. And she has good comic timing when she's reacting to others, but it wasn't called upon enough. Her character's funniest episodes are usually the ones where she interacts with her hilariously awful family members, which brought out Aniston's gifts at being horrified in a funny way.
6) Ross -- David Schwimmer actually has comic talents, but the character was so annoying he didn't get to show them enough. Sometimes he could redeem the character when he got a lot of comedy to do (like in the episode where Ross gets the spray-tan that keeps coming out wrong). But mostly Ross as written was just so whiny and annoying that I would dread it when he took center stage.