Are there levels on Minecraft

Yes and no. In the 1.8.1 patch, Notch released an experience system, and when you kill monsters they will drop some orbs. When you collect these orbs, a little bar under your food and health bar will rise. When it gets to the top, it will start over again. However, you don't really level up, and you don't get any more strength or better armor or anything. But this is probably something that Notch is working on, and hopefully it will be released in the next patch.

EDIT: It is now confirmed that the ability to spend Skill Points will be added in the 1.9 patch.