There are just sooo many subcategories to this,it's just not funny.
I think we can categorically state that giant fighting robots started their life in Japan. RoboTech? is the real defining point for them - humanoid robots twenty feet tall with a single pilot.
TransFormers (RobotsInDisguise?, no less) carried the 'multi-mode fighter' idea a bit too far perhaps.
Both BattleTech and GundamWing decided that pilots was too wimpy a thing, and that the mecha should mimic their controllers actions directly through some sort of brain scan. NeonGenesisEvangelion took this concept to its current peak (though MacrossPlus has a good sequence too)
Orguss? and GunBuster prefer to have large multicrewed robots.
And HeavyGear? of course, has city sized tanks. (And they are mostly tanks - breaking the humanoid mold)
At the other end, we have elementals and (yick) BubblegumCrisis? - ExoSkeletal? systems that are really just armour and weapons rather than a whole extra robot.
There is something interesting that in anime, GiantFightingRobots can dodge and weave and dance (NeonGenesisEvangelion again) whereas in western action (mostly games) they are more like semi-mobile weapons platforms. I'm not sure what this means, if anything. Maybe that the Japanese like ballet a little more than is good for them. Or maybe it doesn't mean anything.
Did I say mostly games? I'm thinking of BattleTech here, of course. A WarGame?. An RPG. Lots more WarGame?s. A CRPG or two. An RTS, a few action games and a quite abysmal squad based Gauntlet clone.
The strange thing is that such robots only really belong in SteamPunk (oh gods, I just remembered ImperialFlowerPatrol?. The pink, the pink! Help me!) since, after all, modern military thought is that specialisation and miniaturisation are the way to go.
RoboTech? gave possibly the only good reason to put such robots in a modern setting. (SpoilerWarning) The things are PowerArmour? for a race that is twenty feet tall. Humanity doesn't realise this.
Oh. I wonder if you can count the CyberMen? in this definition? (And all the other 'war by proxy' androids in SciFi) I mean, if I'm counting bodytight PowerArmour? as sorta GiantFightingRobots despite not being giant then they deserve a mention.
The waldo from Alien? Or are we pushing things too far now?
In closing, I prefer the mind reading dodgy shooty twirly type - preferably that has an AeroSpace? fighter mode. Though turning into a motorcycle too is pushing it.