[NB North American readers should note that the word "guinea pig" here is the European term for "cavy"].
Guinea pigs belong to the Family Caviidae in the mammalian Order Rodentia (rodents). They share most of the general rodent characteristics apart from their curious inability to create their own vitamin C, an inability they share with monkeys, apes and humans (no other creatures in the animal kingdom, at least among the vertebrates, seem to suffer from this). Originally they hailed from warmer parts of the world, but are now commonly bred in the West and like many captive mammals and fish have been diversified into different breeds.
Guinea pigs are one of the most common pets in the UK, probably as popular as rabbits and rats. They are also tagged as a children's pet, and I think this is probably more accurate than it is for rabbits as guinea pigs tend to be gentler and more handleable. However, it is still to much to expect a child to take full responsibility for the regular feeding, watering and particularly cleaning of a guinea pig. There are also several different breeds of guinea pig, plus a large pool of one what might term 'mongrels', ie a mixture of breeds. This should not put you off adopting a mixed-species as they make just as good pets and may actually be sturdier as they have not been exposed to the dangers of pedigree inbreeding. Generally the breeds can all be divided into either long- or short-haired: of the two, short-haired guinea pigs are easier to care as the long-haired varieties need regular grooming to avoid their fur getting knotted and filthy.
The one thing a potential owner should be aware of is that guinea pigs are, through no fault of their own, messy. Thanks partly to their diet they defecate copious amounts of pellets, even more so than rabbits, and as their pellets are usually moist they pile up quickly, get pressed down in the straw and become a magnet for maggots and other problems. Marianne Mays recommends that a guinea pig hutch be cleaned out twice weekly and once a month be thoroughly disinfected. I can certainly vouch from hard experience that leaving the cleaning for more than a couple of weeks can result in a very unpleasant time once you finally tackle it.
Guinea pigs like companionship, although I am not sure what their social structure in the wild is like. Their small size means that two will usually fit comfortably into a hutch as well as one. Two females ("sows") will get along fine, but care should be exercised with two males ("boars") together as they may fight after a while. A male and a female can be accommodated together provided you are aware of the boar's innate drive to mate, which will quickly result in one litter after another. In fact in such a mixed setup it makes sense to separate the female at intervals to allow her to recover, or else to have the boar neutered. The latter is probably more desireable if you want to avoid frequently offloading of young guinea pigs onto pet shops, friends and children from your own children's school: even pedigree breeders don't make much money out of it. You should also be aware that there is a minimum and maximum age for mating female guinea pigs: ignoring this will result in severe damage to or the death of the female. Another alternative is to put a guinea pig in with a rabbit. Provided the guinea pig has a part of the hutch or home to retreat to which the rabbit cannot enter, they normally fare well together. They should be watched, however.
Guinea pigs are herbivorous and generally need a fair amount of fresh food to obtain their vitamin C. It is fairly easy to provide this in the form of vegetables and fruit, even if just offcuts or leaves from the pieces intended for human consumption. Guinea pig mix is also acceptable as most brands have usually been reinforced with vitamin C, but it is unwise to depend upon this. Finally, hay should be provided on a practically unlimited basis: I try to give each of ours a large handful each day. Water is best provided in a rodent bottle hanging on the wire mesh, as in my experience guinea pigs seem to like spilling water everywhere. This also has the advantage that you can add a few drops of vitamin C to the water and know it will eventually be drunk rather than end up in the straw. In practice, feeding and watering guinea pigs is much like doing so for rabbits, except that fresh food is more important for the guinea pigs.
Hutches are easily obtained if you want to keep your guinea pigs outside. Whether you keep them indoors or out, you need to avoid the dirt building up. Apart from being unpleasant for the guinea pig(s), this also constitutes a nuisance to the neighbourhood and potentially a health hazard. Cleaning out once a week is quicker in the long run than spending hours trying to scrape out layers of encrusted muck. You may find that putting a layer of newspaper down first before the straw makes cleaning easier, as you can then simply pull out the paper with all the old mess on top of it. The final point is the reason for hutches, ie the security of the pets. Apart from the fact that you don't want your pet escaping (and possibly nibbling your neighbour's favourite plants, guinea pigs would probably also be targeted by any urban fox in this country. Make sure your hutch is secure. To make doubly sure we actually put padlocks on our hutch doors so that the fox could not work the doors open.
Mays also suggests that guinea pigs can be kept indoors. This is true, but in this case cleanliness becomes even more important as you don't want dirt building up in your kitchen or if you have young children around. It should also be remembered that guinea pigs are rodents, and that the natural propensity of the rodent is to gnaw. Thus guinea pigs running free should either be attended or kept in an area where they cannot gnaw on furniture or cables of any sort. A panicked or excited guinea pig may also expel a pellet of faeces onto the carpet, although this is easily removed.
Are they really children's pets? I think in fact they make good pets for children in view of their size and docility. Mays suggests that five years old is the minimum age for a young guinea pig keeper as younger children might drop the guinea, causing it damage. I am not sure about tameness, since they do not seem as intelligent as rats and our two normally resist being picked up, but other people may have different experiences.
Guinea pigs, then, are good pets provided you can make the time to give them fresh food and regularly clean their home out. Below I have provided links to rabbit-orientated sites written by more knowledgeable keepers which it will be probably be worth your while checking out.
Critter Collection's Guide to Rabbits - recommended as it also includes a page on the many different breeds available.
Pet Centre - this business gives a fairly concise guide to rabbit requirements.
House Rabbit Society - guide to house rabbits, plus many links to other sites.
For children and teenagers:
Animal Aid youth-orientated section on pet rabbits.
Children's Stomping Ground - younger person's guide to rabbits.