Verts
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I'd probably say my favorite all-time shmup has still got to be Dangun Feveron. I'm no Cave fanboy, by any means, but that game in particular is just gold. It plays like one really long time-attack level, minus the time limit. No gimmicks, just blow shit up as fast as possible and collect as many medals (discomen) as you can along the way.
Then I'd have to say Raiden II/DX... because sometimes, I'm masochistic, and like to be slowly and excruciatingly ground into dust by sniper bullets and slow-scrolling backgrounds. :p
Horis
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I have always had a general dislike of the Darius games, but the one exception to that, Darius Gaiden, is probably my favorite all-time hori.
After that, it gets a little muddy. It's a bit of a toss between various arcade and console shooters like R-Type, Thunderforce III/IV, Gate of Thunder, Aldynes, Gradius II, etc.