Giant Robot Games: I need a system edition

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Hey /tg/, I'm interested in playing a game with gigantic robots that may or may not be fighting other gigantic robots and/or monsters.

I'm looking for as much customization of the robots themselves as possible, since the people playing are the same kind of people who kit-bash Gundam kits and build their own parts. They like to customize.

I know there's an Ad Eva system, though I don't know much about it, but I'm not really familiar with any other systems that fit this genre.

Can anybody recommend anything good for me?

Additionally, so we have have some discussion, thread questions:

When was your last giant robot game?
What was the plot like?
Any memorable moments?
What is your favorite giant robot series/game/etc.