Blizzard has just announced a Starter Edition for Diablo III, which lets you play a limited version of the game for free.
There are a few restrictions on the free edition of the game, although there is no time limit.
The restrictions are:
You can only play Act I up to the Skeleton King
There's a level-13 cap
Matchmaking is available only with other Starter Edition players
No Auction House access (real money or Diablo gold).
You do get Global Play and a pretty good taste of the game, though.
To get into the Starter Edition, you can get log into your Battle.net account; create a Battle.net account; or use a friend's disc to install the game. There are more detailed instructions and an FAQ here.
If you do decide to upgrade to the full version of the game, all progress and achievements will carry over.