Actually, most of the
Makaimura games would be
perfect for this. We could see who could reach the highest stage in a given GnG in a single credit. And it's incredibly difficult to be anything resembling "good" at any of those games, so there's no "I'm-a stomp all of you in this game I rock at" issue.
But I still want to see more suggestions. And good ones, too, unlike the things bobbysq1337 mentioned.
I'm going to throw one out here myself:
Blade Buster, a homebrew NES shmup. It's an homage to the
Star Soldier family of shooters, and is just as fun as any of those, but with the enhancement of being a free download.
I played it for a week straight back during STGT2011 over on the system11.org shmups forum, and had an absolute blast. It's easy to learn most of the scoring tricks, though there are some rather odd strategies in there that seem counterintuitive (I've forgotten most of it, myself), and the game itself is less than five minutes long, so restarting due to dying or making a really big mistake isn't nearly the setback it could be in some of the games I'd normally suggest for this. Its length also means you can easily play a credit or two during a break or whatever (especially if you have an NES emulator on some sort of portable platform).