Well, I don't know if the following are my favourite, but they have thus far been very memorable to me:
"DO NOT TEASE THE OCTOPUS" - Ultros (Final Fantasy VI)
"..." - Cloud (Final Fantasy VII)
"Don't you need my brain power?" - Lucca (Chrono Trigger) ~ More like fire power.
"HEY! LISTEN!" - Navi (Ocarina of Time) ~ Probably my least favourite quote.
"Snick! My switch was turned on!" - Burgh (Pokemon Black/White) ~You won't believe how hard I LOL'd when I first heard this.
"This is bad! Bad for Team Plasma! Or Plasbad, for short!" - Team Plasma Grunt (Pokemon Black/White)
"I like shorts! They're comfy and easy to wear!" - Youngster (Pokemon Red/Blue/Yellow)
"Everyone has psychic power. People just don't realize it." - Sabrina (Pokemon Yellow/FR/LG)
"You're too slow!" - Sonic (Super Smash Bros. Brawl)
"Spankety, spankety, spankety!" - Porky (Earthbound)
"here goes no something." - Mr. Saturn (Mother 3)
"we are fulgrate." - Mr. Saturn (Mother 3)
"All the info is there, except for the info that isn't there." - Librarian (Earthbound)
"Yesno, you will won't." - Moonside resident (Earthbound)
"It can dry anything in mere minutes, even long hair, afros, panties, and Asian beauties!" - Dr. Andonuts (Mother 3) ~I know it's racist, but still, LOL.
"YOU REAP WHAT YOU SEW-SO-SO GREETINGS CHEESE POPSICLE THE NUMBER YOU HAVE DIALED IS CURRENTLY OUT OF PORK CHOPS FROM EAST TO WEST IT GOES GOES BROKEN BROKEN OH SO-SO-SEW BROKEN..." - Miss Marshmallow (Mother 3)