OMG, I watched so much (of the same three episodes that I owned) of Cyber CIty Oedo 808.
As for classics, I don't know how well known this one was. A three-part OAV.
Detonator Orgun
Basically the anime that opened me up to mecha. Nothing partiulcar about the story. Dude in future-tokyo dreams big, lives small. One day a super awesome robot (Orgun) comes to town and brings with it an evil super awesome robot that starts tearing stuff up. Dude + ORgun rips evil super awesome robot a new one and a battle for earth starts after that. Some wonderful melodrama in this one.
Trigun
Trigun is Trigun. Awesome western-sci-fi and pressure cooking on melodrama! RIP Wolfwood and thanks for the anime feels.
Dominion Tank Police
A anime cop show about cops in the future driving tanks, which usually leads to massive collateral damage. Followed up by the show "New Dominion Tank Police". I still have these VHS'.
Appleseed
Kind of similar in style to Dominion Tank Police.I remember loving the dynamic between the two main characters.
Now, let's go reeeeaaally far back:
Starzinger
This one I grew up on and watched as a kid. It's called Starzinger in Sweden, wher I live. But I think in the US it was called Spaceketeers or something. However, this one is responsible for the earliest feels in my life and I still appreciate it to this day. I mean, it had grown mean expression powerful emotions, crying their hearts out over tragedies. I'd never seen that in any cartoon before, and it stuck with me. The action was really good for it's time andt the music... oh my god the music... Youtube that sh*t right now!
Other honorable mentions that have been brought up here are Kenshin and slayer.