Although the Steam entry currently does not list either OS as supported, it works on both of them. Linux users can get the game through Steam for Linux beta.
The game is the same, with its dated look. But I still recommend it to anyone who loves the Half-Life series and hasn't played it yet. It's considerably different from its sequels, in the sense that it focuses more on environmental puzzle-solving and has some very difficult bits. The sequels, on the other hand, are more focused on creating an exhilarating action-movie experience for the player.
Half-Life is currently available through Steam for $9.99 (although the price drops considerably during sales). Purchase it once and you can download it on any of your computers running Windows, Mac or Linux.
I have currently not verified whether the Source engine version is available on the two new platforms, but The Verge says that they have tested the linked version. The Source version is not that different, although the water looks a lot more realistic and some weapon models are much more polished and resemble those in Half-Life 2. I would imagine it is available because Valve has been working on porting Source to Linux all along and TF2 for Linux is available already.