A well-maintained board will last a very long time, but wood is a natural product and does require a bit more care than a plastic cutting board.
Wash your board after use
Wooden cutting boards need a wash after use, especially if they've been saturated in oils, juices from meat, or foods that stain.
Never clean your board in the dishwasher or leave it soaking in a sink full of water. The water will deeply penetrate the wood and it will split. Just give the board a quick wash and rinse with warm water and a little soap.
Wood absorbs moisture, which can lead to cracking or mold, so it's important to dry the board after use. After washing, give it a quick wipe down and air-dry in a dish rack. Avoid stuffing it back in the cupboard right away, because there will still be moisture in the board after a wash, even if it feels dry to the touch.
Treat your board with cutting board oil/conditioner
Over time and with use, all wood cutting boards will dry out and need a refresh with cutting board oil or conditioner to help prevent stains and cracks, repel water and keep the board looking great. How often you'll need to do this depends on how often the board is used and can range from once a month to once a year. Make sure the board is clean and dry before applying any oil or conditioner. Use a dry, clean rag or a paper towel and rub enough oil to coat the board's surface on all sides (not just the top and bottom). Don't use regular cooking oil -- it's not the same thing and it will go rancid.
Boards are more prone to staining if they haven't been oiled in a while and lighter woods like maple and cherry will show stains more easily than darker woods like walnut. If (when!) your board gets a stain, combine 2 tablespoons of baking soda, 1 tablespoon of salt and 3 tablespoons hot water to create a non-toxic cleaning agent. Mix these ingredients together to form a paste, and scrub the entire surface of the cutting board. Finally, wipe it with a warm wet cloth and dry. Results may vary, depending on how dark the stain is and how long it had time to set. If the stain has set, I've found that they generally fade over time and with continued use of the board.