I would recommend Gundam Wing, 08th MS Team, 0083, 0080.
Patlabor definitely.
Wasn't a big fan of Eureka Seven, seemed overcomplicated and excessively long, but I saw the edited dub so maybe I missed something (doubt it) If you want something from that studio, I suggest Bounen no Xam'd/Xamdou, however you want to spell it. Not as many mecha, but much more interesting, and the main character isn't a whiny little 8th grader.
Gunbuster 1&2, of course.
Evangelion is more about people, and how incredibly screwed up we all are, than it is about mecha. It is still good. But you must watch it and remember: it isn't ripping off other mecha shows: all other mecha shows are ripping off IT.
Macross
Gurren Lagann, which you absolutely must watch at least once in your life. Also, when watching, relax your brain and don't think too hard. You'll only miss out on the sheer amounts of awesome it contains. Or your head will explode. One or the other.
Gasaraki maybe? I still haven't managed to get a copy of it to watch, but I've always wanted to ever since I saw the VHS previews as a kid.
Escaflowne definitely. One of my all time favorites. Reminds me: I need to re-watch that. Its been like 5 years or something. I really liked the movie, too but they are quite different. The costumes are much better in the movie though. And Van is so much cooler.