I'm usually looking for good cyberpunk, cheesy 80s/90s action, and darker/understated/experimental stuff.   I still couldn't tell someone flat out "I like anime" irl, since that's associated with uguu~  have to qualify the fuck out of it, like i just did.   VIDEO It didn't get a lot of love when it originally was released [despite airing on Cartoon Network], but 
Outlaw Star  is a pretty solid scifi series. 
Then there's quintessential shoujo/mecha anime 
Escaflowne , although I think most everybody's seen that at least once. 
Can't have a recommendation post without 
Patlabor , especially the movies. 
For superior mid-90's mecha, you can't go wrong with 
Martian Successor Nadesico . 
For a series that perfectly captures the mood of Japan at its economic height, there's 
You're Under Arrest , the four-episode OVA and the movie are the best of the bunch.