Notch has said over Twitter that he's fine with people playing it as long as they submit bug reports to him. However, he wants people to only download it from assets.minecraft.net to prevent illegitimate sources from tampering with it and putting in nasty stuff.
So, if you haven't heard, enjoy. Note that there are still bugs, starting with the fact that smelting doesn't work. It doesn't. Brace for a black crash screen if you try it.
I suggest backing up your entire .minecraft folder, but if you like to live dangerously, you don't have to do all that. Find your .minecraft folder -- on Windows, the fastest way to find it is Start > Run and open the location %appdata%/.minecraft/. Navigate to the bin folder, rename minecraft.jar to something else, and then copy the minecraft.jar from the URL above to it.
Launch Minecraft as normal, reset your texture pack to the default (unless your pack is 1.8-compatible), and enjoy. Seed selection for single-player is in the more options submenu when you create a world.