The Nuku Nuku series stars a robot girl. There are three versions to my knowledge.
Bannou Bunka Nekomusume (OVA)
Bannou Bunka Nekomusume (TV series)
Bannou Bunka Nekomusume DASH (OVA)
The TV series and the first OVA uses the same characters, but is a bit different. DASH is entirely revamped, Nuku Nuku is different, but the human characters are still there including the main human character of the previous series being older. You don't have to watch the other two to understand DASH. You don't have to watch the first OVA to get the TV series. I guess all three are pretty standalone, although personally, I like DASH best.
Outlaw Star
Chobits
Astroboy
Rockman/Megaman
That's all I can think of right off the top of my head.