I've just become aware of an apparently Official Free Minecraft Demo that can be downloaded from PCGamer. Thanks to Elemental for the heads up on this! Somehow I completely missed that this was out there until now, is this posted on the Minecraft site anywhere?
It says that it is full featured except that any world you make becomes uneditable after 90 minutes of play. However; you can make as many worlds as you want. Oh yeah, the cows have a PCGamer symbol on their sides, heh heh.
This seems to have become available on the 19th of April 2011 and it's file properties indicate that it is version 1.5 .
This should finally be a useful way for new people to try out the full version without "needing" to pirate the game.