Not all hamsters bite :)
Syrian hamsters, although larger than the other varieties, tend to be a bit prone to biting and can be quite grumpy when being handled. They also seem to be less inclined to learn their names or tricks than the dwarf varieties too, and require a bigger cage. They are slightly less energetic and lively than dwarf varieties. They should be kept on their own, cage should be cleaned once a week as should they all, and they can be expected to live to around 2 - 2 1/2 years.
Chinese Dwarf hamsters are gorgeous and to this very day I have never been bitten by one. They are small, about the size of a mouse, have a short tail and have the longest lifespan at 3+ years. They must be kept alone and are easy to tame and fun to handle. People often say that Dwarf hamsters aren't suitable for children as they are just too quick to handle, but I have never found this to be the case and I have owned nine dwarf hamsters over the years, although they do have lots of energy! They should be kept on their own, as even if from the same litter fighting often occurs many months later, and if it does they need separating immediately.
Here's a video of my rescued / adopted Chinese hamster Pearl who we tamed, being held by my 11 year old cousin:
http://www.youtube.com/watch?v=Jl5nFutuDXM
Russian hamsters can be kept in same-sex pairs or groups as long as they are bought at the same time from the same pet shop - if they are from the same litter even better! They can rarely be a little nippy (in all the times I've owned Russian hamsters only two have ever bitten me) but it doesn't hurt. They also small and quite quick, fun to handle and none of mine have ever been a problem to tame. They live for around 2 1/2 - 3 years.
I've personally never owned Roborovski hamsters but I've heard they can be quite difficult to handle and to tame. They can be kept in same-sex pairs and groups if bought at the same time and need a very escape-proof cage! They also live for around 2 1/2 years.
What about mice?
Mice need as big a cage as possible, but with bar space no larger than 1cm apart. They like to live in same-sex pairs or groups. They are easy to tame, rarely bite and very intelligent. You can teach them all sorts of tricks. Males are lazier than females but also smell more! Their cage should be packed out with stuff; ropes to climb, a wheel, toilet roll tubes, other toys. The only sad thing about mice is that their average lifespan is about 18 months :(
There are always gerbils too? Gerbils are desert animals, so they need a cage with a base deep enough for them to dig in. They need at least 6 inches of substrate to dig in. Gerbilariums work well (see link below), and with two gerbils living in there it only needs cleaning once every month or so, because gerbils are desert animals their urine doesn't smell.
They rarely bite and can live to about 3 - 5 years old and are generally healthy animals. They can be a little tricky to tame, and gentle calm taming should take place over a few months by an adult, with regular handling from your child under adult supervision. Gerbils are very quick, so it's best if you can gerbil-proof a small room in the house where you can let the gerbils free and crawl up to you and explore, but only do this when they are tame and you are confident handling and catching them.
Madagascan Hissing Cockroaches? You need a tank, extra heating over the winter in the form of a heat mat (stuck to the back or side), couple of inches of substrate and some hides. They are fun to handle and, until tamed, produce an awesome hissing noise! They can't hurt you in any way and are surprisingly cute :P
Photo of mine:
http://www.hencam.co.uk/hencam_forum/extensions/InlineImages/image.php?AttachmentID=1037
Hope this helps :)