I LOVE MECHA! I mean, just look at my profile pic, that's supposed to be me cosplaying as Domon from G Gundam xD
And for my favorite mecha games, I'm going to choose the following:
Gundam Breaker 3 (Vita): I love the customization, creating your own Gundam is really fun and, while I prefer Breaker 2's campaign, I think that Breaker 3's campaign isn't bad, just a little repetitive sometimes.
Tech Romancer (DC): basically a Super Robot Wars game made by Capcom, it's a great homage to several mecha shows, the graphics are good, the soundtrack is great, I like most of the stories, and you can play as Jin Saotome from Cyberbots too! I'm so sad it wasn't ported to PCs with the recent collection... ç.ç
Super Robot Wars J (GBA): this game. THIS. FREAKING. GAME. This game was one of the catalysts for my transformation into a mecha fan, thanks to SRW J I discovered Mazinkaiser, G Gundam, Tekkaman Blade, Nadesico, and the game is GREAT! Probably one of the better gateway entries in the Super Robot Wars franchise, not being too hard but not too easy either.
Metal Bringer (PC): one I recently finished, and I had a blast! Metal Bringer starts kinda slow, with you having access to a Labor (basically a android body) and having to deal with Arms (the giant robots) while using whatever you can find at the time (so... heavy machinery), but with time you can get A LOT of good pieces to use, you can create your own Arms to explore the randomly generated areas and destroy the enemies in seconds. It is a time sink, but I highly recommend!
For honorable mentions I'm going to say Super Robot Wars: Original Generation (GBA) for introducing me to the SRW franchise and Zone of the Enders: The 2nd Runner (PS2) that I love it even if I played the PS3 version without any patches.