Most any Mac OS X compatible External DVD Drive will work with your iMac.iMac, Mac Mini, iPad, iPods, Mac OS X (10.6.8), (10.8.2), Safari, iTunes, iPhoto
1. Go into Spotlight from the top of your iMac on the menue bar.
2. And search for "CDs & DVDs" (It's also in the System Preferences)
Click on it and a small CDs & DVDs window will pop up with options of what happens when you insert a disk into the drive
3. By then, try inserting a disk in (while that window is open. This kinda wakes up your drive to accept the disk). It should accept it.
4. If nothing happens, then manually open the program that should be opening when you insert the disk or go to Finder (Eg. if it's an audio disk, then open iTunes)
5. If opening the program still does not activate the drive to start spinning the disk, then close the programs and windows you opened, and repeat step 1-4 and the disk should be spinning and automatically opening the proper program.
Yes, you could get a USB external disk drive. (It's simply a device that reads CDs & DVDs except it's outside your computer and plugs into your computer through USB) I don't know what it's called but a simple Google search for keywords: external disk drive dvd rewritter superdrive
Apple sells one called SuperDrive. But I believe other brands sell the same device cheaper. It's just Apple's SuperDrive is really thin and looks tight. But you can get other good looking ones too.
Hope that helps!