Rats need to gnaw or grind their teeth frequently in order to prevent their front teeth from over-growing. Some old rats, especially those who have had strokes, may permanently lose the power to chew properly: in this case they will need a soft diet (catfood, pasta, bread-and-milk, cooked oatmeal etc.) and will probably need their front teeth clipping about once a fortnight.
If a rat is off its food or eating awkwardly, the first thing you should do is check the teeth for overgrowth.
A rat's teeth will not wear down properly unless the top and bottom incisors meet squarely. In some older rats the teeth become a little loose in their sockets and the paired bottom incisors begin to splay out. As a result they no longer wear down to a straight edge: instead the bottom teeth spread and grow past the sides of the top teeth, forming long spikes which must be clipped regularly to prevent them from chafing the rat's cheeks. At the same time the top teeth are sharpened to a spike pointing down into the gap between the lower incisors: this spike will also need to be trimmed every couple of weeks.
One cause of loose teeth is an abscess at the root of the tooth. In this case you will usually see pus oozing out around the root, and pressure in the abscess can be relieved by pressing the swelling very gently to express the contents. Systemic (i.e. injected or swallowed) antibiotics may help, but abscesses around the head are never a good sign - see section on infections.
Overgrowth may also occur as a result of a broken tooth. If one of the front teeth snaps - or worse still is lost in some way - then the matching tooth in the other jaw will have nothing to grind against and will rapidly become too long and need clipping.
Clipping of overgrown teeth can be done with some types of nail-clipper or with a pair of small-beaked wire-cutters: whatever clipper you use must be small enough to fit round the teeth and still be able to see what you're doing, and sharp and powerful enough to cut the tooth rather than break it. If in doubt as to how long or short to cut the teeth, look in another rat's mouth for comparison and err slightly on the side of length - and be careful not to nick the tongue. The individual teeth are wider from front to back than from side to side, so if you are trimming one tooth on its own, rather than a pair together, it is usually more efficient to point beaked clippers into the mouth rather than across it, so the blades are pressing against the long sides of the tooth rather than its short front and back.
If you do cut a tooth too short - or split it - and make it bleed this will hurt, but does not seem to do so as much as a broken claw. I suppose that any animal that can chew through sheet metal can't afford to have very sensitive teeth.
The rate at which overgrowth occurs varies from case to case, but on a rough average you can expect to have to cut the affected tooth or teeth back about every ten to fourteen days.
I have never seen or heard of a case of overgrowth of the cheek teeth in a rat, but if it should occur then, as with rabbits, it would probably have to be clipped back under general anaesthetic owing to the extreme narrowness of the mouth, the unco-operativeness of the patient and the way folds of lip tuck in behind the incisors and conceal the back teeth from view.