You are Gordon Freeman, a supergeek scientist at a government research facility located in Black Mesa Bumfvck-middle-of-nowhere. Experiment goes horribly wrong, ripping hole in space, weird creatures start teleporting in and killing everything in sight. You run run run away, pick up weapons, shoot things, and find out that the government has decided to lock down the facility by killing EVERYONE inside (especially you). Meanwhile, there's some mysterious guy in a suit who casually struts around the place while aliens rip apart humans. You jump through a bunch of hoops, get some really cool weapons, eventually are sent to the "otherworld" (named ZEN or XEN or something like that) to do something (I can't remember what - probably to close the space rift), and end up killing a giant floating alien baby thingie.
Then the guy with the suit appears and offers you a job working for "them." You never find out who "They" are. If you accept, end of story. If you refuse, you wake up surrounded by a zillion alien creatures, and you presumably die.
Don't really remember much about Blue shift (where you play a security guard) or Opposing Force (where you play one of the soldiers assigned to "cleanse" Black Mesa).