Shmups that suck but you can't help but like

[nZero]

Star Soldier: Vanishing Earth

great caravan

[Zengeku3]

Dimahoo, Armed Police Batrider and other shmups without good solid characters like Kogs

[EmperorIng]

- annoying final boss "duel"

Annoying!? How!? It's so damn cool!

I agree, but I feel like it's hampered by the final boss being inconsistent with how it wants to open up to you. It's still the perfect way to end the game. The game's presentation is ace, even if its rank makes stage 3-on monumentally difficult.

Metal Black
This STG is basically an RPG you only play for the story.

First time I've ever heard that, and that's not too far off the mark! Though I still am working on getting my score higher...

Lessee,

Sol Divide is fun once in a blue moon, if you blind yourself to the fact that it's junk.

I'm on the fence on whether or not GRID Seeker Project STORM HAMMER sucks or not, and that usually flips back and forth between plays, but I still can get a kick out of it, despite its practically-worthless gimmick (GRIDs should never be anywhere but in front of you), bosses with one attack that take forever to kill, and enormous hitbox. I'm kinda funny like that. You need autofire, I think, to enjoy it. The stages and enemy formations are actually pretty cool.

[chum]

Definitely Batrider. The scope of its stupidity is on another level, yet it's one of my favorite games.

Oh, and Zombie Nation, Mahou Daisakusen and Metal Black fit the bill.

[Pteriforever]

Arkxon, Ougon, and Resurrection of Heaven's Liquor.