Recommended Dreamcast titles?

[VeganZombie]

Alright, I've got a good collection of shmups going, but I'd like to know if there's any out there that I've overlooked...

So far I've got:

Bangai-O
Border Down
Chaos Field
Giga Wing 2
Ikaruga
Karous
Mars Matrix
Triggerheart Exelica
Under Defeat
Zero Gunner 2

And I'll soon be getting:
Gunbird 2
Radilgy/Radirgy?

Are there any other games I should look into for the Dreamcast?

If not, I've got a PS2 as well and I'd like to know if there are any good titles worth picking up that don't involve modding my PS2. I don't have the willpower to tear it open and install a mod-chip.

Hell, PC shmups work too.

[Ayanami]

I like Trizeal a lot, but it is not every one's cup of tea. I would definitely get Gunbird 2 for sure.

While it may not be considered a shooter. I would also look for Cannon Spike. That game is sweet.

[Thunder Force]

Are there any other games I should look into for the Dreamcast?

This is a frequently asked question, so it's probably more useful for you to peruse existing threads via the Forum Search feature, to reduce duplication. (Ditto for recommended PS2 shmups.)