The Running Surface
The best kind of hamster wheel has a solid surface (not rungs) that either attaches to the side of the cage or is free standing without side supports than span the wheel opening. The common wire wheel that looks like a ladder wrapped into a circle with side bars for support is not the best choice as it can cause injuries.
Keeping in mind hamsters are nocturnal and generally use their wheel a lot at night, you definitely want a quiet wheel. This is especially true if you share your room with a hamster! A squirt of vegetable oil is a safe option for greasing squeaky wheels.
I can't find any absolute recommendations for minimum sizes of exercise wheels. Most marketed for hamsters will be suitable, keeping in mind that the smaller wheels are best suited to dwarf hamsters only, and larger hamster wheels should be used for Syrian (golden, teddy bear, etc) hamsters. Get the largest hamster wheel that you can, since a wheel that is too large shouldn't pose problems, but a wheel that is too small will be uncomfortable for your hamster.
Alternatives to Wheels
The run-about balls for exercise outside of the cage are popular, but given the amount of running most hamsters like to do won't really provide sufficient exercise on their own. As a novelty or additional means of exercise they are fine, though. These are available as a simple ball, a wheel shape that propels a car frame and other novelty shapes. There is also now a track system that you can set up to keep your hamster's movements in a run-about contained. Be careful not to leave a hamster in one of these balls for too long or they may overheat (15-20 minutes at a time is plenty), and never use them around stairs that the hamster could tumble down.
Versatile Wheels - Any Cage Type
- Wodent Wheel popular, ASPCA-approved wheel, and the 8 inch size is generous for most hamsters. Free standing. The unique front is semi-solid with holes for access (susceptible to chewing). Vendor's Site
- Super Pet Silent Spinner: available in various sizes; the 6.5 inch model would be great for dwarf hamsters but might be too small for larger Syrian hamsters (the next size up is a very large 12 inches). This wheel uses ball bearings for quiet operation. Can safely be used free standing or attached to the cage bars. Vendor's Site
- Comfort Wheel: the large size is 8.5 inches in diameter, which is a good size for Syrians, and quite inexpensive. Can be used free standing or attached to cage. Vendor's Site
Specialty Wheels for Modular Cage Systems
These wheels expand your hamsters modular home by attaching externally. However, these wheels have the same problems as plastic modular cages in general: they are poorly ventilated (could potentially get overheated) and more difficult to clean.
- Super Pet CritterTrail Snap on Wheel: 6.75 inch wheel that attaches to the side of CritterTrail system cages as well as CritterTrail Fun-nel tubes. Best for dwarf hamsters as it is quite small. Vendor's Site
- S.A.M. Workout Wheel: compatible with S.A.M. cage systems, this wheel that attaches to the outside of the cage. Small size best suited for dwarf hamsters.
- Super Pet CritterTrail Xtreme Wheel - unique-looking wheel from CritterTrail that attaches via a Fun-nel tube. Vendor's Site
Run-About Balls and More
These shouldn't replace having a wheel available in the cage. Free-wheeling run-about should never be used around stairs. Some hamsters will not care much for the balls, and they shouldn't be left in them for long as overheating can be a concern.
- Run-About Ball: the classic spherical run-about. The 7 inch size is great for dwarf hamsters and perhaps smaller Syrian hamsters, but owners of larger hamsters should consider the larger 11.5 inch model. Vendor's Site
- Critter Cruiser: a car shaped frame supports a translucent plastic wheel, and as the hamster runs the car can move. Several settings allow the cruiser to be used either "free-wheeling" or on a track. Alternatively, it can be set for stationary use. The small size of this makes it best suited to dwarf hamsters though. Vendor's Site
- Hamtrac: a nifty system that can be used with a run about balls or a Critter Cruiser -- sold separately. Interlocking plastic pieces form an oval "race" track. Vendor's Site