If you're looking for a squat variation that's tougher than a regular squat, but does not require weights -- you should definitely try the air/jump squat. You'll feel to burn after a few sets of these suckers.
If you really want to really intensify your workout, you can also do other power bodyweight exercises like burpees and mountain climbers.
Here's How To Do Them:
1) Stand with your feet shoulder-width apart.
2) Start by doing a regular squat, then engage your core and jump up explosively.
3) When you land, lower your body back into the squat position to complete one rep.
4) Land as quietly as possible, which requires control.