When should cutting boards be replaced?

The USDA suggests that "all plastic and wooden cutting boards wear out over time. Once cutting boards become excessively worn or develop hard-to-clean grooves, they should be discarded."

Other advice they offer for avoiding food contamination from cutting boards:

Avoid Cross-Contamination The Meat and Poultry Hotline says that consumers may use wood or a nonporous surface for cutting raw meat and poultry. However, consider using one cutting board for fresh produce and bread and a separate one for raw meat, poultry, and seafood. This will prevent bacteria on a cutting board that is used for raw meat, poultry, or seafood from contaminating a food that requires no further cooking.

Cleaning Cutting Boards To keep all cutting boards clean, the Hotline recommends washing them with hot, soapy water after each use; then rinse with clear water and air dry or pat dry with clean paper towels. Nonporous acrylic, plastic, or glass boards and solid wood boards can be washed in a dishwasher (laminated boards may crack and split).

Both wooden and plastic cutting boards can be sanitized with a solution of 1 tablespoon of unscented, liquid chlorine bleach per gallon of water. Flood the surface with the bleach solution and allow it to stand for several minutes. Rinse with clear water and air dry or pat dry with clean paper towels.

The simple rule is that if a cutting board has obvious damage to the surface, it's probably unsafe to continue using it.

The most common such damage is scratches or grooves worn in by your knives, or actual cracks in the material, but any kind of narrow damage is bad; it's hard to effectively clean and can indeed harbor bacteria. The exception is wider wear, like a shallow but smooth worn-down area, which you can still clean. It's easy to tell the difference: if you can't clean it, it'll stay discolored in the grooves, making them very visible. A very worn cutting board will have so many scratches that they start to blend together, turning into a slightly rough, discolored region.

If it's a wooden cutting board and you're well-equipped, you may not have to replace it, though. You can sand it down to remove the damage, rather than discarding it. This depends on the wood; in some cases you may have trouble getting as good a finish as it originally had. While you can do it completely by hand, it's easiest to keep it flat with planer (or at least a belt or disc sander). See for example this What's Cooking America article or this workshop's article.

(None of the safety information is directly taken from a single source; the obvious one is the USDA article on cutting board and food safety that Jeff's answer replicates, but you can find the same advice virtually anywhere that discusses cutting board food safety, like this Consumer Search article - it's all common knowledge at this point.)