Rodents belong in the Order Rodentia. Rabbits are not considered rodents but belong in the Order Lagamorpha. Rodents have one pair of incisors in each jaw but rabbits have two pairs of upper incisors. Their teeth grow continuously, unlike in humans (we only have one set of milk teeth and one set of permanant teeth). Thus, it is possible for their teeth to break and grow back to its original length or even longer. This special trait of rodents means that some teeth can grow too long. This happens when the animals' teeth are not in line and this condition is called malocclusion. Usually, the teeth have to be regularly trimmed by a veteranarian.

There are many different species of rodents (around 1,500 have been discovered) and many of you will know or have personal experiences with many of them. Beloved pets that are rodents include mice, rats, hamsters, chipmunks, squirrels, guinea pigs, chinchillas and gerbils. Many are also considered pests like mice and rats, but some, like prairie dogs and chinchillas are endangered in the wild. Chinchillas are classed under Appendix I of CITES (the Convention on International Trade in Endangered Species of Wild Fauna and Flora).

Rodents are mostly herbivores, or omnivores.

Some references: 

References are cited in order of author, year of publishing, title, publishing house and ISBN number, where known or available. 
Techinical details and study text:  
1. Young, J.Z. 1995. The life of vertebrates. Third Edition. Clarendon Press, Oxford. ISBN: 0198571739 
Leisure reading and information: 
1. Rodents of the world.

Links

1. CITES

2. Rodents at the Animal Diversity Web

3. More pictures of rodents from the U.S. Fish & Wildlife Service's image library.