One of the stand out mods would be the Black Mesa project - whereby Half Life 1 is being remade into the Source engine, used to make Half Life 2. It takes part in the realms of Half Life 2, but from memory the location doesn't appear in the full game. It is possible to play this on the PC (as someone has managed to port it onto the PC). It takes place during the events of the first game. This is a coop game mode available on the Half-Life PS2 release. Someone has already mentioned ' Half-Life Decay'. Half-Life 2 Episode 2 - Continue as Gordon Freeman after the events of Half-Life 2 Episode 1.Half-Life 2 Episode 1 - Continue as Gordon Freeman after the events of Half-Life 2.Half-Life 2 - Years later you take control of Gordon Freeman in a new story.Half-Life: Blue-Shift - You play as a security guard during the events of the original game.Half-Life: Opposing Forces - You play as one of the marines during the events of the original game.Half-Life - You take control of Gordon Freeman in the Black Mesa facility.This is assuming you want to follow the Half Life story from start to finish.

As already pointed out, the most logical order is to play the games by their initial release dates.