Voles (and perhaps field mice) are the biggest pest problem. They burrow under the roots and eat not only the fibrous roots but the basal plate as well. Generally, this damage is performed in the winter when the plants are dormant. Most of the plants damaged in this way will live but will be much reduced in size. If you suspect voles, dig the plant and examine the roots. The lack of roots will be obvious and the rodent's teeth marks on the basal plate are frequently visible. Luckily, voles are fairly easily controlled by putting poison seed (which can be obtained in most garden centers) in their holes/burrows. Snakes are also fond of small rodents.
For another effective method that we employ, refer to the following:
Organic Vole & Mouse Control - Castor Oil Treatment
Richard Merritt's New Hampshire Hosta method works, effectively eliminating vole damage.