quick question: does anyone know of a service that serves free (as in »free beer«) art (paintings, photography, illustrations etc.) to download in high resolution so you can print them yourself?
Not a unified one, however most museums have decent interfaces to their collections these days. I would highly recommend the Met Museum in New York's catalog, for instance. Some produce limited resolutions or force you to decode some kind of image-slicing, but in general you can get super high resolution copies for free that would be suitable for personal use.
Google images is great for that. Search by keywords, then set the minimum resolution under "Search Tools". 8 megapixels should be enough for a good print. 20 megapixels - for huge ones.