aside from what everyone says (evangelion, etc)
I think MuvLuv Total Eclipse is Awesome, and Gunparade March, i watched, it's pretty good...
I really like the more Realistic approach, more than the "super robot" theme...
Also Fullmetal Panic / Gundam 00 / Eureka 7 Ao

Sorry, but I have to say that in my mind Gurren Lagann trumps all the other mecha animes.

What other mecha anime has epic quotes like that?

Gundam will definitely have to be my first (mostly because of 00, Unicorn, and Seed)
Full metal panic series altogether as a close second.
And then Infinite Stratos just because of the way the mechs are designed and the concept of them being armor is just too awesome.

Also forgot Total Eclipse, Gurren Lagann, Vandread (only cause of the comedy), IGPX (tho i barely remember it now), and DEFINITELY Evangelion.

Gasaraki and Flag have realistic approaches to mechas. No 'super robots' in those. I wouldn't call Evangelion truly mecha genre because the Evas are basically cyborgs, not robots. Though there was Jet Alone (unmanned giant robot) in one of the episodes, which had a nuclear reactor for a core... smart...

Fun fact: If you do the right steps in Evangelions 2, you can get Jet Alone as a final stage reinforcement. But wait! It's been upgraded and now wields a hammer. OF JUSTICE. (Also; the final stage is the fight with the MP Evas from EoE.)

Anyway, for me personally:

Vandread (I liked it for primarily the character interactions. I did think the mecha stuff was fine although it did suffer from turn of the century CGI though. We never will get a Third Stage, will we? The manga's terrible though. I'd say it's close to Nadesico manga level bad IMO.)

Linebarrels of Iron (While I still prefer the manga by a vast margin, the anime was fairly interesting. I'm not sure how I feel about Yamashita in the anime though. It's also brought up a nice possibility the original world the Machina came from in the anime might actually be a slightly different manga verse. Especially considering the last episode had the one or two shots of what could Proto-Linebarrel and the characters inside it had a very strong resemblance to the manga designs of Kouichi and Emi.)

Burst Angel (Holy crap. I love this show, as mediocre as it was. I really liked the whole western feel they had going on with Jango and some of the music too. My only major complaint was the pacing was a little awkward sometimes and they spent a lot of time fiddling around when they could have been doing the main plot. Then there was the OVA and the teasing of a possible second season which we will never get. Also; manga pretty much confirms Meg and Jo.)

Star Driver

Rahxephon was the perfect blending of Mecha and Music. It's a classic and how unfair is it that people always disregard the show due to copying claims.

G gundam....no Gundam Wing.....no Zoids
You know what nevermind.
Sorry, I can't choose in this type of situation

1. Eureka Seven
2. Gurren Lagann
3. Code Geass

People have already named the mainstream ones that are good so I'll skip those

some lesser known ones that are also good:

Gunbuster
After War Gundam X
Bokurano (do not watch if you're not into psychological/pressure/sad stuff)
The Big O

Eureka 7, Evangelion, The Big O

Yea i really liked Gundam Seed and Zoids

Gurren Lagann, Code Geass, all of the Gundam releases in their own right, M.D. Geist (Powered suits count), Vision of Escaflowne, Gasaraki, and the epicly beautiful anime short: Voices of a Distant Star.

The MS IGLOO releases are a personal favorite of mine just for their very interesting "the unsung heroes of an era" story telling approach.

Oh yeah and Blue Gender. The fact that the romance between the two protagonists actually becomes a conclusive relationship well before the end of the show is in itself enough of an accomplishment to merit a place in the list. I am quite sick of the oblivious guy who misses 1,000,000 chances with the love of his life because he is a helpless goofball formula.

And Macross Plus... How did I forget that? I keep having to add more with edit lol.