There are plenty of series like that.
Tengen Toppa Gurren Lagann, Fafner, and RahXephon come to mind as especially exceptional mech series.
Code Geass and Star Driver are technically that too, although to a lesser extent; they're more about the characters than the mechs (though actually that holds true for any good mech series). As acolyte mentioned, Evangelion, Eureka Seven, and Macross Frontier are must-watches and if you're into the mech style, there is no reason not to check out Gunbuster, Diebuster or both.
