Well, I used to be obsessed with a game called "Quack Shot" as a kid, I never owned it, but played it at m' cousins house. It was for the Sega Genesis...and it was like the first video game I ever played...
But, if thats not what you meant by your question, I've always wanted to play/own Orcarina of Time.
Hundreds of NES, SNES, N64, Genesis, and other titles... Dreamcast and PS1 too.
Final Fantasy I, II, III, IV, V, VI, VII, VIII, IX
Samba De Amigo
Blast Corps (well, I played it, but I want to own it)
Rez
Phantasy Star Online
Bionic Commando
Chrono Trigger
...You know, I'm going to stop right there. That's just like a millionth of my list.