There is a large variety of bedding/nesting material available on the market for hamsters, and it can be difficult to decide which is most suitable for your pet.
"Fluffy bedding" is one of the most commonly sold beddings for hamsters, this is the coloured cotton wool texture, made from artificial fibres. Many people buy this as it looks lovely and snuggly for hammies to make a bed in, and although the vast majority will have no problems, it is safer to avoid. One of the problems with artificial fibres is that if they tangle around a limb, it will not snap. There have been reports of hamsters losing legs as the blood supply has been cut off. Another problem is that it is indigestable, and hamsters can accidentally swallow portions which block their digestive systems.
Natural cotton fibre bedding is also available, and is suggested as a safe alternative to fluffy bedding. Concerns about tangling and indigestability also exist with this bedding, so I would advise people to err on the side of caution and avoid this.
Commercial safe beddings
My current bedding of choice is safebed paper wool. It is long, soft strips of paper, seems long lasting (I have found other paper beddings are quickly soiled) and quite popular with the hamsters. If for any reason I have been unable to get safebed, my backup is Pets At Home safe bedding. I don't like this quite as much, as the small shreds seem to be trickier for the hamsters to build their nests out of, but it is certainly safe and cosy. There are many brands of "paper wool", either long strips or small fragments, any of these make excellent nesting material.
Some shops sell shredded paper bedding, some people prefer this as it is available in a range of colours. I personally don't think it is quite as cosy as the paper wool, so don't use it.
J-cloth bedding, which looks like sections of shredded j-cloth is also thought of as a safe bedding. It is cosy, soft, but has a tendancy to spred everywhere all over the house.
"DIY" safe bedding
One very popular and cheap hamster bedding is shredded value toilet roll. For syrians and larger dwarfs, whole sheets can be given and the hamster allowed to make its own bed. For roborovskis or smaller dwarfs, this should be torn into slightly smaller strips. Kitchen roll is less suitable, as it will not be digested as quickly.