I think some other points need mentioning here.
1- Gordon has clearly been chosen as a pawn who can be bought and sold at will by whomever wants him. Breen knew about this. If Breen knows then the Combine knows. If the Combine knows its not to far to think the vortigaunts know as well. The reason Gordon has been chosen as this pawn is because he can be 'the right man in the wrong place'. He has the ability to manipulate events around him to such an extent that the G-man/any one else with his contract is almost assured of the success of their plans by working them through Gordon.
2- Alyx is similar to Gordon. I don't beleive she is on a contract per-se, but she is clearly important to either 1) the G-man and his long-term goals or 2) the success of Gordon and whatever plans are designated for him. Obviously the G-man/his employers knew of her importance back at the black mesa incident and this is the reason she was kept alive
3- Shepard is also similar. Shepard is also more important and critical to the events of HL1 than people realise. Gordon (unwittingly) set most of the plans up, and got as far as being able to access xen to destroy that particular race of aliens, but Shepard finished the job. Shepard was required to stabilise events at black mesa after Gordon had left, and was most likely needed in order to give the G-man access to the bomb which destroyed black mesa. Shepard will be needed again, how or why is open to speculation.
4- Half-Life as a name for the series most likely came from the fact that the 'A' in 'Half' is the lambda symbol which is also the symbol on the nuclear reactor in HL1, nuclear, half-life. Simple.
5- No-one seems to consider the amount of time which passes between HL1 and HL2. My guess is a few years at most, although this does mean that Alyx would have to be pretty old at the time of HL1 in order to be the age she is now. Correct me if I'm wrong (and I might be on this detail), but the picture Eli has in his office of his family was taken sometime around the black mesa incident? I can't remember exactly. If that is true then at least 20 years would have had to have passed in order for Alyx to be that age, but that doesn't seem to fit with the other chracters ages.
6- Gordon has not been seen since he stepped into the portal to go to xen near the end of HL1 until he stepped onto the train in HL2. During this time he most likely has been held in a stasis field, preventing age etc, much the same as is what is currently happening to Shepard. Gordon was merely held, like you would turn your computer off, until his time was needed (turn your computer on).
7- In HL1 the G-man is simply observing Gordon/Shepard, but with the knowledge that both of them would be needed in the future. Same goes for Alyx. She only lived in order to be of use later on.
8- Not sure if this matters or not, but in Opposing Force when you first get into the game there is a scene where one of those blue aliens grabs a scientist in another room then warps out with the scientist. Apparently, that particular alien model had the same eye structure as the aliens in HL1 did (ie like a segmented bugs eye). The NEXT time you see the same alien model, it has one eye in the middle of its body identical to a human one, as do many of the other alien models in the game from then on in. The theory going around witht that is that the alien combined with the human, which is what gave it human eyes compared to its normal bug one.
9- Referring to point 8, the Combine are an amalgamation of human and aliens. Striders, dropships, hunters and the such are all actually living creatures (much evidence for this in games, especially episode two when dog rips the striders brain out). Although unlikely, it is possible that black mesa was destroyed by the G-man in order to prevent an joining of human and aliens (similar to that observed in opposing force) as such a unison would be bad for him/his employers.
10- Again, not sure if it is important, but at the end of HL1 one of the scenes in xen when the G-man is talking to you shows dead soldiers and a downed plane. Obviously they had either already previously taken the fight to xen, or pulled out of black mesa (forget about freeman!) in order to fight them there. Again, probably not important, but worth considering.
11- The advisors seem to share similar (although not as advanced) powers as the G-man. They're obviously psychokinetic (as demonstrated by the ability to control and issue orders to combine troops in ep2) and can also pick people up in mid air and the such. My guess as a story arc is the G-man/whoever he works for is trying to prevent the advisors/combine from gaining similar sort of power to what the G-man possesses. (Teleports, stopping time). If that means destroying the combine (who have only limited teleportation technology so far, remember they needed the black mesa incident in order to be able to come to this world) and using Gordon as their pawn then so be it.
12- Why are the vortigaunts good in HL2? I never sort of figured that out, especially after being a bad guy in HL1. The G-man himself makes reference to this. The vortigaunts were originally part of the xen species of aliens, yet showed no glimpses of the obvious power they possess in HL2. They have existed as a species for quite some time (one of them talks about herding antlions for their essense in ep2) but it seems like more of a storyline glitch than anything else.
13- The vortigaunts are able to negate the G-mans power somehow. Although it looks like they can't touch him and he can't touch them. They're sort of like two chess players who have to use pieces in order to beat the other. Gordon, Alyx, Shepard, probably even Barney and others are all merely pieces.
14- As to who the G-man is, I think he controls certain peoples lives and sells their contracts to the highest bidder. Its obvious he scouted Gordon/Shepard but also needed them in order to carry out what happened at black mesa. He most likely has a great deal of prescience (his version of the vortisessence which is mentioned in ep2) and knows who he must control in order to acheive the future he sees. As to what that future is... who knows.