I have the Big Robots, Cool Starships supplement for BESM but I was wondering if anyone had a good supplement or suggestion for a Mecha book.

How is the Robotech book?

I'm looking for something sci-fi with giant robots and space ships, handsome fighter pilots wooing beautiful vixens, tough as nails power-armored marines blasting away at the enemies...

you get the idea.

Honestly you have just named my suggestion, mecha is great in BESM

There was a system I used once that I would love to find again. It was called Mekton Zeta. Really awesome system for running mechs.

The "Camelot Trigger" setting for FATE is made specifically for mecha, but I haven't played it yet myself.

The Robotech rpg (both old and new editions) uses the Palladium system (or at least a close enough iteration that differences aren't worth mentioning), and if you're familiar with the system you'll know if that's a good or bad thing depending on your own preferences.  If you're not familiar with it, then you might want to look into it or start a separate discussion.

If you want a game set in the Robotech setting they make great source books even if you run using another system.

Mekton Zeta/Mekton Zeta Plus run using the Fuzion system.  It's a pretty universal mecha game so you can do a lot of types of genres with it.  Plodding Battletech style mechs, transforming Robotech styles, and even Sentai type combiners.  The base Mekton Zeta game is a full game, but Mekton Zeta Plus cranks up a lot of the crunch factor with a lot of options for building your custom mecha.  The system can be numbers intensive, especially if you get into custom mecha designs and the like but the many years ago that I played it, I remember it running fairly well.  It'll do your space opera oriented mecha game fairly well as I think there's some rule for spaceships and such in one of the books if they're to matter more than as a backdrop.

They Kickstarted an updated version of Mekton somewhat recently but it's still in production I believe.  However the original games are still available for sale in pdf.

There's the Mecha rpg, by Chris Perrin.  I've never had the chance to play it but it looks interesting with mechanics that seem somewhat streamlined and some story gaming elements.

I'm sure there's a couple more specific games I've heard of that I'm simply forgetting about.  There's also the universal systems that can run Mecha games (Gurps, Hero, etc).

If I may ask another question in this topic, what would be a good one for a Pacific Rim type game? I was thinking of looking up the Mekton Zeta books, but if there's a better system, I could go for that.

there are rules for armours in Tenra Bansho Zero

but other than b-tech and mechwarrior that is my only experience with mechs.

and in my opinion TBZ can do no wrong

Apotheosis Drive X is another FATE based Mecha game.

I remember seeing Cthulutech's mecha rules recommended as pretty good as well, though I've never had the chance to try them out myself.

Cthulutech's mecha rules are very nice... but the subject matter is much darker than what you're going for, I think.

If you can snag Adeptus Evangelion, thats a pretty cool mecha system. Reliant on the 40K rpgs as a base though.

The best I saw was homebrew and lost to time but we made our own system where all the races had there own kind of mechs with there own abilities.

Well, GURPS has gotten better since they stopped using calculus for vehicles. Not even I thought it was neat to go into that much detail. So they had 8 books or so on various space ships, and included Mecha designs. There was a pyramid article that expanded on it (called Modular Mecha) and made mecha almost worthwile for someone like me that generally doesn't like Mecha.

There is also Remnants, which I think is an interesting little system (haven't had the chance to really play), but it isn't your typical mecha game. Your "mech" is actually attuned to you and can improve through play in various ways that don't involve engineering upgrades to it. It almost seems a bit nanotech in how improvements are described. Also, the mechs in general are not huge (although there are exceptions) and the game is a alternate post-apocalyptic setting. The core book IIRC is fairly inexpensive and there are probably quick-start rules out there too.