Air Fortress (NES)
I'm pretty sure this counts. One of my favorites on the console actually.
I have no idea why, but for some reason... even just flying around in this game is still a complete blast to me.
MagMax (NES)
This one is really cool in how it's sorta like R-Type with the multiple ship powerups, but instead of powerups, you get different body parts for your robot, which you can combine in all different sorts of ways. What's also cool is that you are often given plenty of opportunities to warp underground or above ground during each level - which really makes each playthrough a unique experience depending on your chosen route.
Adventures of Dino Riki (NES)
Honestly don't know why I thought of this, because I haven't played it since trading it into FuncoLand long, long ago. But it definitely fits the bill, I remember enjoying it at the time, and finding it fairly challenging/frustrating.
and last but not least, my absolute FAVORITE non-spaceship shmup.....
*drumroll*
Capcom's Gunsmoke (also on the NES)
This game is great! Cool weapons, interesting levels, fun boss battles, and you even get to ride a fucking horse! I'm no cowboy-nut, but this one probably gets played by me more than any other NES cart that I own.
Really, really cool music too.
Forgotten Worlds (GEN), and the clunkier than all hell Rainbow Cotton (DC) also come to mind. As does Astro Boy (GBA) but I've never played it.