Lock-On (Arcade).. fun arcade first person futuristic jet shooter. I used to be addicted to this.
(no video available)
Speed Buggy (Arcade/C64/Amiga, all good versions, Tatsumi.. Amiga is probably the best one which is actually controllable at home)
http://www.youtube.com/watch?v=8YQo3hVfvIw
This is an excellent racing/obstacle course game. It's really addictive.
Hot Rod - Arcade .. I don't know that I can rightfully call this one obscure, but it never really got a good home port and most people haven't heard of it. It's still an excellent game. It's like Sprint, but a lot more entertaining in my opinion. Or, like a non-crappy Moto Roader.
(see? not even a mame video

Realm of Impossibility (C64)
Seriously, seriously, amazingly overlooked. This is a gem that's a lot of fun with two people. You run through surreal M.C. Escher-like mazes, grabbing treasure, and foiling enemies. You can't shoot enemies, but you can drop crosses which freeze them in their tracks. You can also pick up and cast spells.
http://www.youtube.com/watch?v=LdGBA0FG7Gk#t=2m
Ninja Gaiden - Arcade. OK, I'm one of the only people who think this is better than the generic home Ninja Gaiden games. But it is! It's one of those rare beat 'em ups with really solid "I'm getting hit because I messed up, not because it's random" gameplay. So, it's got goofy enemies and runs choppy. So what!

http://www.youtube.com/watch?v=UaO0M8THQoM#t=1m30s
Breach 2 (Amiga)
This is a great squad strategy game. If you like X-Com, you need to play this. The level editor used to keep me busy for hours. Screw Laser Squad!
Six-Gun Shootout (C64/Apple)
Great strategy game with detailed rules which simulates popular old west battles. Nobody knows this, but they know Law of the West :/
Psi-5 Trading Co. (C64)
Sweet space trading game where you have to run a starcraft populated by your eccentric crew, battling pirates along the way to deliver goods.
http://www.youtube.com/watch?v=Yre8waZlJSI
Arcade Game Construction Kit (C64)
I don't think many people know about this one (compared to SEUCK). It lets you design classic style arcade games with all different kind of AI patterns and goals. You can even do Gauntlet-esque games or side view platformers with all kinds of switches. I sunk an unbelievable amount of hours into this, and it's got groovy title screen music too.
Park Patrol (C64)
Fun game where you're a park ranger rescuing people in a raft. I think it's pretty obscure, but fun. It's one of the last classic style Activision games. I almost didn't include this, but I didn't have the heart

http://www.youtube.com/watch?v=-k-dReIfz00
EDIT: Added more vids
