I have a waterproof/breathable rain jacket which has a few holes in it (caused by a minor bicycle crash, in case that information is relevant). They are not too big, about 5mm across. How can I patch these holes? It doesn't have to look too pretty, I'd just like it to be reasonably waterproof.
If it doesn't need to be pretty, a cost effective option is spinnaker repair tape (nylon cloth tape, for example, see products on this page). It is designed for repairs to yacht sails so it is durable, weatherproof and should survive a machine wash (but it wont be breathable). Stick a piece over the hole on the front and back of the fabric.
Some stores have waterproof glue which you could use to fix a waterproof patch. An example.