Wheels and Run-Abouts
Most hamsters make great use of a hamster wheel and your hamster's cage should have a wheel if possible. It is important to make sure the wheel is the proper size and try to get a solid surface wheel to cut down the risk of injuries. Run-Abouts are the clear plastic balls (several styles are available) in which you put your hamster and let them run around on the floor without worry of them getting away on you. Both wheels and run-abouts are great ways to make sure your hamster gets enough exercise, and more advice on choosing a wheel or run-about is found in "Hamster Wheels and Run-Abouts."
Hamsters, as will all rodents, need a good supply of items and toys they they can gnaw on to keep their constantly growing teeth in good condition.
Wooden pet chew toys are an ideal choice. Wood items should ideally be safe (stay away from cedar or other evergreen type woods), and pesticide and chemical free. If you are unsure a type of wood is safe, it is probably best to stick with items made for use by pets. Pesticide-free fruit tree branches from your backyard or hardwood wood blocks or shapes that are not chemically treated are okay for your hamster.
Willow balls, rings and tunnels are also marketed for rabbits, and the smaller sized of these items can be used for hamsters.
In addition to wood chews, cardboard can also be provided for chewing (and for hiding). Ideally, choose cardboard with as little ink as possible as there has been concern over the content of commercial inks in the past (I can find no solid evidence one way or the other on the safety of colored cardboard, and I have used colored cardboard for my mice, so don't panic if you are using colored cardboard). Hamsters also love cardboard tubes from paper towel and toilet paper rolls, although some people are also concerned about the safety of the glues used in these. Many hamsters regularly chew these items without problems, but if you are concerned there are now commercial tubes that are a bit sturdier and are said to be safe for chewing (e.g. Totally Chewbular Play Tubes and Critter Crunchy Chew Tube).
Climbing and Houses
There are also a variety of climbers and houses/huts designed for hamsters and other small rodents. Wood ladders and climbing blocks are great for hamsters. If you can't find wood ladders in the hamster section of your pet store, check the bird section. Any of these wooden items are bound to be chewed as well, as that is natural for hamsters, so be prepared to replace them as needed.
You can also use hardwood dowels and wood to made your own ramps and climbing structures. Coconut shells can also be used to create huts and houses. Organic ropes (hemp, sisal, cotton) can also be used to construct hanging toys, walkways and bridges in the hamster cage. Extreme caution is required with hanging toys and ropes -- use thicker sizes of rope and be absolutely sure your hamster (head, body, legs or toenails) can not get entangled in any ropes used to hang items, or use them only under close supervision.
Caution is needed when it comes to plastic. Most hamsters love plastic tunnels and tubes and other play structures, but chewing can be a problem. Some plastic toys will be destroyed very quickly, and if you hamster is swallowing plastic pieces from chewing, that is a big concern. When you offer plastic items, keep a close eye on them and if your hamster is chewing too much, remove the item.
Sand and Digging
You can provide a dish of chinchilla dust bath or fine sand, in which you hamster may roll to keep its coat in good condition. Also, most hamsters love to dig so providing a deeper box of sand or sterilized soil big enough for the hamster to burrow in is a great treat for hamsters.
Mineral Blocks, Pumice Stones
These are not really necessary. If your hamster does gnaw on them it can help keep their teeth in good condition, but they are very hard and many hamsters won't really use them. A variety of natural wood chew items is a better option (and necessary minerals should be provided via the diet).