Old school favorites:
Lifeforce/Salamander for NES
For nostalgia - not a particularly difficult game. Loved that it mixed horizontal and vertical scrolling levels in the same game.
DoDonPachi (favorite bullet hell)
This is just a classic, found an arcade in Taiwan that actually had it and played the "bullet hell" out of it.
Mushihimesama because I secretly hate myself.
Apogee's Raptor: Call of the Shadows (loved upgrading my weapons in that game)
And basically every Touhou game for the art style and music.
Finally a personal favorite (I'll be impressed if anyone else here has played it):
Steel Empire for the Sega Genesis