1988 was the year of awesome new IPs as well as amazing departure sequels that were nothing like their ancestors.
Altered Beast
Bad Dudes vs. Dragon Ninja (the original Japanese arcade title)
Battle Chess
Bionic Commando
Blaster Master
Castlevania II: Simon's Quest (U.S. release)
Double Dragon II: The Revenge
Dragon Warrior III
Famicom Wars
Final Fantasy II
Ghouls 'n Ghosts
Golgo 13: Top Secret Episode
Golvellius
Gradius II (NES port)
Ice Hockey
Iron Tank
Kenseiden
Mega Man 2
NARC
Ninja Gaiden
Nobunaga's Ambition
P.O.W.: Prisoners of War
Parodius
Phantasy Star
THE POWER PAD with World Class Track Meet (U.S. release)
Power Strike
R.C. Pro-Am
Rock Star Ate My Hamster
Shinobi
Splatterhouse
Super Contra (arcade version)
Super Mario Bros. 2
Super Mario Bros. 3 (Japanese release)
T&C Surf Designs
Track & Field II
Ultima V
Ys II
Zelda II: The Adventure of Link (U.S. release)