Pretty much your favorite "anything" having to do with shmups and most importantly... WHY?
If enough people post, this can be a kinda neat topic and a good learning experience for some.
Thanks for contributing...
*****EDIT*****
Gee... I made the topic but didn't even say my favorites! So, here I go.
Favorite shmup (one I have most fun with): Space Megaforce/Super Aleste
--Why? Well, I really enjoy how the different difficulties aren't just "more bullets" or "faster enemies." It's usually a combination of both, or slower bullets... or something that will force me to change my playing style and use different weapons.
Most appreciated shmup (one that shows some originality): Ikaruga
--Why? It seems like the only shmup that can truly be mastered. It takes lots of repetition and training... but if you're good you can get huge chains, and really feel like you accomplished something. (It's tough.. my highest chain was 29 I think...

Best Company:Compile
--Why? They really cranked out those shmups on the MSX. Guardic, Zanac, Aleste 2. Guardic offered very non-linear play, and the zanac/aleste series had gobs of weapons!
Best Platform (from personal experience): Super Nintendo
--Why? Uh... because my Saturn can't play imports, and I don't have a Dreamcast... But seriously, I have Space Megaforce, R-Type III, Axelay, Gradius III (better than the arcade version), and a couple of descent Darius games. So, I think it's an ok handfull of shmups.