What is the maximum mass of a satellite that can be placed in GEO? Or can satellites of any mass be placed in GEO?
Assuming orbital assembly (with separate launch vehicles, each delivering a portion of the total mass of the satellite), there is no real upper limit, short of technical limitations that we're currently struggling with. At least not until you orbit such a huge mass, that you literally start playing the game of pool with celestial bodies, permanently destabilize their orbits, cause extinction level event and terminate any life on the Earth as we know it due to gravitational pull between two objects (the Earth and the satellite) so huge, they start "feeding" on each other's mass by forming an accretion disk connecting the two, and suffocate their own atmospheres with it (among a plethora of other undesirable side effects).
The GEO orbited mass could as well be larger than the total mass of the Earth, and we have Charon, locked in the skies of Pluto as a proof of that. Pluto and Charon are tidally locked in a synchronous orbit, meaning they always face each other with the same side (as do the Earth and our Moon), but also synchronously orbiting each other (Pluto orbits a point that is outside its body), meaning Charon is locked in the skies of Pluto as a rock that's been frozen in motion, and Pluto is locked in the skies of Charon. Charon has approximately 11.65% of the mass of Pluto, meaning Pluto has about 8.6 times the mass of Charon, yet it's still technically in a GEO orbit "around" it.
Cosmic dance, face to face: Two bodies with different mass ratios orbiting around a common barycenter. Any of these three
mass ratios could be tidally locked in synchronous orbits, always facing each other with the same side. (Animations: Wikipedia)
Similar was believed for Mercury orbiting the Sun, and that it might be tidally locked with the Sun, always facing it with the same side, but that was later disproved by radar observations in 1965. Strictly theoretically speaking though, it would have been perfectly possible.
So, in short, there is no upper limit to total mass that can be put in GEO. If your mass comes mostly from the Earth itself, then it would obviously have to be smaller than the total mass of it (poor Earth, people should learn to travel light), but if you bring mass from elsewhere (other celestial bodies, maybe asteroids, or the Moon itself?), then your upper mass limit is the patience of the humankind to tolerate your endeavours and the problems they bring along.
Having too large of a mass would, of course, change requirements of the GEO orbit itself, destabilize the Earth's rotation on it's axis (day/night and seasons of the year cycles) and around the Sun (length of year and seasons), change the tidal patterns (that we do depend upon), accelerate atmospheric loss, and all kinds of other uncomfortable side effects.
As of Early 2015, the maximum payload to GEO is 6750 KG using Delta IV Heavy.
To take TildalWave's answer a little farther: Eventually you'll have enough mass up there that Earth enters the Roche limit of the object you built--goodbye Earth. You'll need something well above Earth's mass for that to happen, though.