Golden Sun series
Phantasy Star series
Shining Force series
Star Wars Shadows of the Empire (a personal fav, but probably not objectively a great game)
Mystical Ninja Starring Goemon / Goemon's Great Adventure
Wave Race 64 + GCN
Ogre Battle Series
Shadowgate (NES + N64)
Lufia series (SNES, GBC, GBA)
... too many more for me to remember.
(Time has sorta forgotten these below to any young generations of gamers but but I'm sure they'll still be in the hearts of millions)
Yes, Lemmings definitely belongs on this list. It was a bit before my time but I first played the PC version back in 1997 at a friend's place and instantly fell in love with it. I know that it was super popular in the early 90's and was basically the original Angry Birds. It's too bad that it is now largely forgotten. Another great early PC game was the Even More Incredible Machine.