I have a long list.
Any Final Fantasy deserves on here however, I think
Final Fantasy VI has the best ending I have seen. It caps off the story perfectly, pushes the SNES to new limits during the credits, and has a nice touch of everything.
Final Fantasy IX has the best line in post VI series ("no cloud, nor squall..") and the FMV right after that is simply amazing, if the game was a as amazing as VI, this would of beat out VI as my favorite.
Final Fantasy X - really picked the game up
The other (Final Fantasy) also had great endings and are tops on my list
Lunar (both versions)
Lunar 2 (both versions)
Super Mario 3
Ninja Gaiden 1 & 2
Kingdom Hearts 2 (that song will not get out of my head)
Dragon Warrior III & IV
Earthbound
Street Fighter 2 "series" - Ryu's ending, Zangeif's ending is pretty good too
Chrono Trigger
Breath of Fire 2
Mortal Kombat IV - Scorpion ending getting revenge on Quan Chi
Starcraft and Brood War
Startropics
Tekken series - endings are great in general, 3 allows you to watch them all
Final Fantasy Tactics
Wild Arms 3
Super Mario Bros 2
Contra
Phantasy Star IV
Ergheiz - Sephiroth ending montage, its like a one minute greatest hits video
Mega Man 3 - gave the series a bit of a story
Secret of Mana (Seiken Denretsu 2)
Final Fantasy Adventure (Seiken Denretsu)
Suikoden 1, 2, 5