Which anime would you guys recommend to someone (me) who only watches it for the fights?
I've not seen a lot, but I have seen (and loved) Dragon Ball Z, Hunter X Hunter, Fullmetal Alchemist. I know One Piece is meant to be good but 600+ episodes to catch up is on too much for me.
I would prefer a longer series but just not 500+ episodes long.
Baccano
Blue Exorcist: The Movie (action isn't the highlight, but it's not bad)
Code:Breaker
Dirty Pair (TV, OVA, and Project Eden movie)
Fate/Zero
Fullmetal Alchemist: Sacred Star of Milos (also, if you're only watched one out of the 2003 or Brotherhood TV series, you should go watch the other one)
Garo the Animation (the first anime series with its upcoming sequel film Divine Flame, not Garo: Crimson Moon)
Gintama (if you just want the fights, you can watch the serious arcs)
Gunslinger Girl (not really based in action, but what action is there is quite good)
Hunter X Hunter: If you've only watched the 2011 series, watch the 1999 series (or vice versa)
Jojo's Bizarre Adventure: both OVA and TV
Kizuna Ichigeki
Majin Bone
One Piece Film Z (the TV series is not worth watching in its entierty, but this and some of the other movies/specials are worth checking out for action)
Skull Man
You Are Umasou (really!)
Yozakura Quartet: Hana no Uta
Yuu Yuu Hakusho
That should be enough for starters.