You can easily go to the openstreetmap.org front page and print it from your browser. You get a reasonably good-looking map that is often better rendered than Google Maps or the other competition. However, because it's printed out from the bitmap tiles, it's not quite such good quality as your printer is capable of.
In theory you should be able to export a PDF and print that... but I have found it difficult to get one of the right size, or send it to the printer without odd errors. Is there a foolproof way to 'download PDF of the current view' but using your normal paper size (A4 or US-Letter)?