Well, I notice a lot of these suggestions are from when anime got a bit larger in popularity. Some suggestions have been redone (or are in the process of being redone) like Hunter X Hunter (previously mentioned), Hellsing (which is being released in a series of movies closer to the actual manga), Berserk (not berserker [ugh]) (which is currently being made into a 3 part movie series, no idea when it's supposed to be released).
Trigun is easily one of my favorite older anime series (it even had a movie come out semi-recently). Gundam is probably my favorite 'old' anime series, and there's a LOT of those to go through if you choose to. I also want to second the Outlaw Star suggestion (just make SURE you get the missing ep 24(?) (Hot Spring Planet Tenrei) episode if you watch it, as it explains some things that you would otherwise miss since the episode was nixed for the US audience when it was aired on TV. The original Ghost in the Shell movie was awesome, but it was re-released as a 2.0 version with some redone scenes (not to be confused with GitS: Innocence, which is Ghost in the Shell 2, basically). I would also REALLY recommend the Bubblegum Crisis series (and as a follow-up the AD Police Files series set in the same world).