In that case, they already exist
You can have your very own for just 36 million yen.
Damned giant robots. Get off my lawn!
You might be thinking of ASIMO, who’s not commercially available. (He’s also more child-sized than man-sized, but that’s another story.)
Wow, how cool is that? Here’s the company’s website. It’s mostly in Japanese, but it includes a longish movie of the robot walking (sloooowly).
Exactly.
A giant mech would concentrate hundreds of tons on two feet. It would sink on any unpaved terrain. I doubt it would do to well on paved terrain either.
It would present a much larger target to the enemy.
Factor in the inertia of all that mass. It could easily be out manuvered by geeps, tanks, planes, helicopters etc.
Unless you added more crew to man extra weapon positions, and added extra weapons (more weight), and more ammunition (more weight), a few soldiers on foot and armed with rpgs, portable missile launchers, etc could surround and destroy it.
Taking out a foot, ankle, knee, or hip would severely reduce the mech’s capabilities. Taking out the other foot, ankle, knee or hip would knock the mech over, render it all but immobile, and make it a giant sitting duck.
Any improvements in armor, weapons etc to compensate for these shortcomings would make much more sense to apply to tanks, etc.
lol, when I started this thread these were pretty much the kinds of answers I was looking for, but now that you guys have provided them so thoroughly, I regret it. My childhood heros are being reasoned out of existence! 
Bipedalism is a pretty difficult and unstable way to get around. If you are designing for functionality, for most purposes it’s going to be better to use wheeled or tracked locomotion on level terrain, or quadrupedal or hexapedal locomotion on rough terrain.
There are basically just two reasons to make a robot look humanoid, that is, be bipedal.
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So it can use equipment or fit in vehicles designed for humans.
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Because it’s cool.
If you made a robot much bigger than a human, you would negate reason 1. And so far, reason 2 hasn’t outweighed the enormous technical problems and costs involved in making such a robot - nor are they likely to in the future, except for a millionaire mad scientist.
There’s a second video, also, showing the operator firing the robot’s weapons (such as they are). I was amused to note that the target has a Space Invader painted on it. 
We don’t have giant robots for the same reson we don’t have giant insects, or for that matter, supergiant land animals(anymore) - weight scales approximately with the cube of size (i.e. it is proportional to the volume of the body), strength only with the square of size(i.e. it is proportional to the cross-sectional area of the muscles, or the equivalent of muscles); a giant robot 50 metres tall will have about half the ‘scale’ strength of one that is 25 metres tall.
Then there’s the properties of the construction materials; a large crane has less ‘scale’ rigidity and physical strength than a smaller one that is a scale model in every detail.
So you could build a giant robot, but on its own scale, it would just be a huge, flaccid weakling.
What if we gave it a bunch of Enzyte?
Well, I suppose you could send it multiple spam emails to that effect and see if it bites; “experience more powerful hydraulics!” or “become the giant robot that feminine giant robots will desire!”.
On a related note, what about non-giant mechanical exoskeletons for infantry? Am I correct in assuming that the main issue is the lack of a lasting power supply small and light enough to power such a device? Is it also considered simply more economical to build a few costly vehicles than to design, build, and support an army’s worth of “powered armor” suits?
Catalyst
The seventies had the Hardiman project. The goal was a powered exoskeleton with the arms and legs capable of lifting IIRC a ton each. After a few years and much money, they had an exoskeleton with one arm capable of lifting 1200 pounds and three nonfunctional limbs.
DARPA remained interested in exoskeletons, particularly ones for the lower body that would increase speed and range. There have been several successful projects in this area. All of them involve simple mechanical solutions- springs etc.
How about this? not humanoid, but it walks on legs:
http://forevergeek.com/gadgets/the_walking_forest_machine.php
Listen, dude, you know how much giant robots would cost. It would cost in the bilions I’m sure no Congress, Senate, or President in their right mind would approve of such a bill. It would be cool, though, I admit.
Berkeley is developing exoskeletons for DARPA:
http://bleex.me.berkeley.edu/bleex.htm
The idea is to build something to increase the endurance of a soldier. Apparently, back of the envelope calculations show that an exoskeleton that would permit one to leap buildings would tear its occupant apart.
NASA has built a 50 foot robot with CalTech, but there’s a big coverup. Ok, actually there is not a coverup. Oh, and the robot is made of flowers. http://slashdot.org/articles/04/12/31/1926249.shtml?tid=216&tid=133
Then there are the enthusiasts:
http://neogentronyx.com/
http://www.mechaps.com/
hijack - you must be joking - have you ever seen the latest appropriation bills just passed? £5 billion to build 5 nuclear reactors in China as one example. Give me a 100 ft killer robot instead anyday for the same money.
The military is currently developing combat robots for under the Future Combat Systems program. These robots, such as the MULE, all use fairly conventional wheeled or tracked chassis. I wouldn’t expect to see a Gundam-styled bipedal combat robot for a very long time.
As the technologies improve, I wouldn’t be surprised to see smaller legged robots developed for scouting roles. Legs can cross difficult terrain that’s impassible to a wheeled vehicle. I can see the benefit of having small, legged robots that can drag themselves into places to perform a reconnaissance or light support mission that something with wheels cannot. Take something like that Japanese Land Walker robot, mount some cameras and a laser designator, a 50-cal, and maybe an RPG launcher and it could make itself useful supporting infantry in a rugged or urban environment where even a Humvee couldn’t go.