Why does my iMac freeze up?

Key points to check are heat, hard drive and ram. Power is also a possibility, but let's start easy.

iMacs are prone to heat problems causing the processor to overheat, and even the hard drive to overheat. The cooling is definitely my first suggestion. There is a vent along the top of the back panel, and also a circle vent near the mount to the foot on the back panel. There are vents along the bottom side of the iMac too. Canned air may blow out some dust, but an air compressor at 20-40psi will make quick work of it.

You can usually check your hard drive SMART status from Disk Utility. If it's reporting any Reallocated Sectors, Current Pending Sectors, or worse yet Uncorrectable Sectors, then it's time for a new hard drive. Get your data off while you still can.

While you're in Disk Utility, verify your OSX and check the Disk health

Ram can also crash a computer. If you're using more than one stick of RAM, try using just one stick to test. If it still crashes try the other. Try alternating sockets too.

Hope this helps a bit. Happy repairs!

-Toupee Scalper