Blizzard, a video game developer and publisher, has considered the option for years, and it dabbled with a number of free trial programs, all of which were time-limited.
Now, under the new program called World of Warcraft Starter Edition, new players can play at their own pace without having to worry that the free trial will expire. When they reach level 20, they can continue playing but will stop earning experience, making it impossible to level up. To play past level 20, new players will need to upgrade to the full version of the game, which can be done online here.
Although there's no time limit for trial players, there's a great deal of other restrictions besides the 20-level limit: Trial players can have a maximum of 100 gold; their trade skills are capped at 100 ranks; they are unable to trade in the Auction House or join guilds; their chat options are limited; and they cannot invite other players into a party and so on.
In short, the game itself may be free, but it's a far cry from the full World of Warcraft experience.
Here's an FAQ describing all the intricacies of the new free trial system. To sign up, go here.