The clumping cat litter type should not be used, as it can be accidentally ingested and can cause harm to your rats. The compressed paper pellets such as Yesterday's News are safe to use, and make good bedding. Since it is rather hard to sleep on, you should provide another type of nesting material or a hammock to keep the rats comfortable while they sleep.
Wood shavings are cheap and absorb urine easily. Cedar and pine chips cause respiratory infections in rats and can be lethal, so don't use them. There aren't many other disadvantages of wood shavings except that they tend to get kicked out of wire cages more frequently than other types of litter. The best kind of wood is aspen, which you can find at most pet stores.
Carefresh is a brand of recycled paper product that is soft and contains no chemicals that can harm your pet. It is sterilized so you can be sure no pests are entering your rodent’s cage. It also comes in different colors! It is probably the most expensive bedding, though effective, and it can get kicked out of the cage fairly easily because it is so light.
If you get a newspaper or flyers in the mail, shred them up with a paper shredder or by hand into long strips. They aren't as absorbent as some of the other kinds of bedding, but since they are usually free and readily available, if they get soiled they can easily be replaced more often. Since it is light, it can fly out of the cage more easily if your cage bars are wider spaced.
Rabbit or guinea pig food pellets can also be used as rat litter. They are just as absorbent as other pelleted litters but are normally much cheaper, and for people who already have rabbits or guinea pigs they are readily available. Rats generally do not eat them, as they contain ingredients that rats don't care for, but if the rats do eat them it is all right.
Even non-breeding rats like to nest, as it is one of the natural instincts of a rat to burrow or pile up soft materials to make him or herself a safe and comfortable place to sleep. Providing a smaller portion of a different, softer, kind of bedding can help your rats be comfortable in their beds. Carefresh, while expensive for entire cage bedding, makes good nesting material as it is very soft and absorbant. Shredded paper towels or toilet paper, or strips of a non-fraying material such as polar fleece can also be used.