Please stop. everyone. I an get that popularity of Gainax's Neon Genesis Evangelion, FLCL and Gurren Lagann... But best anime ever? none of them are even worth being called best mecha anime ever. By the way, for all EVA fans: Space Runaway Ideon.
The real list should look close to this
1. Hokuto no Ken: Think Mad Max, where the protagonist is an unstoppable kill machine, and basically Jesus.
2. Mobile Suit Zeta Gundam: The Second gundam series, and the one that is still considered the most influential in terms of groundbreaking mech designs and beautiful, yet depressing storylines.
3. Cowboy Bebop: Too fucking cool for words, one of the most impressive English casts in anime history.
4. Black Lagoon: Basically Cowboy Bebop, set in the 21st century. Oh, and one of the best dubs I've heard. Maryke Hendriske should be in every anime.
5. Kaiji: Fuck you idiots who think Death Note and Code Geass were "psychological" this my friends, is a REAL psychological show.
5 for now.