Minecraft.net allows you to play minecraft classic without downloading anything, all you need is Java applet.
If you're stuck on the demo mode after purchasing Minecraft, please visit this article. before deciding to make a purchase, you can play the demo mode by registering for an account, then downloading the Minecraft launcher.
You can play the demo mode of Minecraft for PC and Mac by registering for a Mojang account and then downloading the Minecraft launcher. This version of the. How to Play Minecraft For free No Download