Check out XBox Live Arcade. They are remaking a lot of the classics with improved graphics, sound, and even game play and I must say I've been having a blast with them the past month.
SF II HDRemix
Ninja Turtles IV Re-Shelled (tons of fun if you have someone to play it with you)
1942 Joint Strike (An absolute blast if you have someone to win it with you)
R-Type
Geometry Wars HD
Puzzle Games (tons of them)
and many more.
You should really go browse through them. That said, I'm with you on the newer game thing. Ninja Gaiden II and Mass Effect.. Ahhhhh, yeah buddy. Good memories tied to those.