Yes, trapping can be effective in controlling rodent infestations. We assume you are referring to commensal rodents such as mice or rats. For other rodent species (squirrels, muskrats, pocket gophers, nutria, beaver), trapping is certainly effective.
For commensal rodents, trapping is most effective when the problem is localized, such as in a home or when the quantity of mice/rats is low, such as when trying to prevent reinfestation.
The key to effective trapping is to use enough traps (most people use too few), to properly place them, and to properly maintain them. Placing traps strategically where rodents have been noticed is very effective and inexpensive. Set the traps inside containers to prevent non-target captures. Bait stations are typically designed to allow snap traps to be placed inside.
References:
Mouse Control
