Unlike curtains, doormats don't need a tape measure and a calculator - they come in a handful of standard sizes, and picking the right one is really about matching the size to where it's going. Here's a quick room-by-room guide.
Your front door gets the most foot traffic and the most dirt, so go bigger here - a 21x31 inch mat gives visitors room for a couple of steps before they're on your floor, which is what actually keeps dust and mud out.
Bedrooms don't need a heavy-duty mat - a smaller 15x22 or 16x22 inch cotton mat beside the bed is soft underfoot and easy to shake out or wash.
100% cotton doormats work well just outside a bathroom too, since cotton soaks up water quickly. A 15x22 inch size is usually enough to cover the spot right where you step out.
A 16x24 inch mat in front of the sink or stove gives you enough length to stand comfortably, and cotton is easy to wash after spills.
Cotton doormats are machine washable in cold water - wash separately for the first few washes since dyed cotton can bleed slightly, and air dry rather than using high heat to keep the weave from shrinking.