As already pointed out, the most logical order is to play the games by their initial release dates. This is assuming you want to follow the Half Life story from start to finish.
- Half-Life - You take control of Gordon Freeman in the Black Mesa facility
- Half-Life: Opposing Forces - You play as one of the marines during the events of the original game
- Half-Life: Blue-Shift - You play as a security guard during the events of the original game
- Half-Life 2 - Years later you take control of Gordon Freeman in a new story
- Half-Life 2 Episode 1 - Continue as Gordon Freeman after the events of Half-Life 2
- Half-Life 2 Episode 2 - Continue as Gordon Freeman after the events of Half-Life 2 Episode 1
Someone has already mentioned "Half-Life Decay". This is a coop game mode available on the Half-Life PS2 release. It takes place during the events of the first game. It is possible to play this on the PC (as someone has managed to port it onto the PC).
Lost Coast is a very short demo. It takes part in the realms of Half Life 2, but from memory the location doesn't appear in the full game.
Half-Life also has a rich mod community. One of the stand out mods would be the Black Mesa project - whereby Half Life 1 is being remade into the Source engine. The difference between this mod and the Half-Life: Source release is that the graphics are being completely polished.
Depending on your tolerance, or appreciation, for older games, it is feasible to completely skip Half Life 1, or at least the expansions. They were great games but are still old games. Not to say Half Life 2 isn't an old game.
Will you miss anything not playing Half-Life 1? Not really. The story in Half-Life 2 is so different. A different time, a different location, different enemies... If Half-Life 1 never existed, Half-Life 2 would still be a great game and story.
If you play Half-Life 2 then the episodes are worth going through as they immediately follow events from the main game. There is also a cliff-hanger at the end of Episode 2. Episode 3 never appeared and people have been waiting a generation for the next installment.
Portal has been mentioned but the game is not like Half-Life. Don't assume that you MUST play Portal 1 and/or 2 because you played Half-Life.