I have two guesses as to who the G-Man really is:
1: An alien, representing some omnipotent alien force which has yet to reveal itself.
2: A representative of an organization of a high-technological secret human bureaucracy, like the Men in Black or the X-Men, who have dealt with the paranormal since the 50s.
Whatever the case, his employers seem to take an interest maintaing interdimensional control, and especially in individuals who are most useful in helping them bring about that control. His employers probably took interest in Black Mesa’s studies of Xen, and was sent first to deliver the Nihilinth crystal sample as a business transaction, then to argue with the Black Mesa staff against testing the sample through the high energy beam because of the cosmic repercussions it would cause. Why he dealt with them the crystal, and then warning them against using it, I am uncertain.
Contrary to what some believe, I don’t think he’s an agent for the Combine. He summoned Gordon specifically to destroy the power center of City 17 to cripple to Combine’s control. Why? Again, because his employers want to keep the Border World critters from messing things up interdimensionally. They found Gordon attractive, because he took out the Nihilinth who was causing the interdimensional rifts, and thereby brough Xen under his employers control. Why did they want it? Probably as as satellite base in the Border Worlds.
Who are the various parties who are vying for Gordon’s services? I know that Breen implies that he is aware that Gordon was employed, and suggests that the G-Man’s employers act more like an auction service agency concerned more with supplying agents to powerful bidders rather than maintaining stability. However, the unknown bidders may be other aliens who see Gordon as a means to clean up their own Combine problem. This leads to the question: if Gordon’s employer’s are only an auction agency, why then did they send him to disrupt the Combine? Could it be that his stunt in City 17 was merely a showcase by the G-Man and his employers to potential bidders?
Whoever Gordon was originally supposed to be sold to, the Vortigaunts now have repossessed Gordon, and the G-Man is forced to recognize their hold on him, either by the Vortigaunts, his employers, or both.
As you can see, the clues are getting more complicated as the game series progress. What’s clear at the moment is that the bureaucracy he represents had particular intentions for Gordon, and it is implied that Eli with the Vortigaunts’ help snatched him away too soon before the intended moment for Gordon’s use had arrived. Whether he had something to do with the assault on Eli by Combine Advisors, I’m not sure. It’s likely that the G-Man was aware that the Combine knew that Gordon was supposed to be tucked away for a very long time, and that Vance was responsible for keeping him awake in during his time period to mess things up even more for them. It seems like the G-Man didn’t interfere, because any interference on his part would have directed the Combine’s anger towards him and his organization, and also because he wanted to make his point to Gordon and others that Eli’s interference will render matters even more difficult for them.
For me, the G-Man’s character later on feels like a cross between J. Edgar Hoover, William Parcher who is another G-Man from John Nash’s hallucinations in a Beautiful Mind, and Moebius the Time Streamer from the Legacy of Kain series. He’s such an ominous and freaky guy, that I’m dying to see what part he’ll play in the next HL episode.