Puzzle game-inspired shooters.

[Drum]

I really like Dan Da Dan http://www.youtube.com/watch?v=08prtYUKx2Y and Space Invaders Extreme. And I kind of like Wacko http://www.youtube.com/watch?v=1372rtQaXf0. Twinkle Star Sprites probably qualifies and Bangai-o at times (to its detriment mostly, but whatever). Anything else like them? They don't have to be match-colour games. Nobody say Ikaruga or Cave games >:(

[dieKatze88]

Space Invaders Extreme 2 is one of my favorite things about my Nintendo DS.

[Mortificator]

Quarth.

[Annoyboy]

Radiant Silvergun?

[MathU]

Don't forget Space Invaders Extreme 2, though it's a little less puzzle-y than the first game.

[Obiwanshinobi]

There's a "puzzle" stage in Shikigami no Shiro II.
Not sure how to label Space Bomber. Sandbox shmup?
I consider Magical Drop III as a shmup-inspired puzzler.

[Zaarock]

Radiant Silvergun?

Less of a puzzle game than Ikaruga at least.. you basically just kill red enemies and blow up bosses, not much thinking to it.

[Despatche]

The term "puzzle" clearly sucks.

[BulletMagnet]

I consider Magical Drop III as a shmup-inspired puzzler.

That manner of definition would open the door to plenty of others - Landmaker and Zoop come most immediately to mind.

In any event, apart from those already mentioned, two games I'd personally consider "bona fide" puzzle/shooter crossovers are Calcolo and Finger Flashing, both for the PS1 - I blogged about both (along with other puzzle games) some time ago, here and here respectively.

[Treasurance]

That Holy Hell game
oh wait it's the other way around

[BPzeBanshee]

Volfied. As to whether it's a puzzle-inspired shooter or a shooter-inspired puzzle, that's another story.