The tag says "Dry Clean Only" but the curtains are 100% cotton with no pleating that could potentially be ruined in the wash. The consensus of my five minute search seems to be about 50/50, meaning 50% of the curtain-cleaning population encourages you to give it a try, and the remaining 50% advise you to heed the label.
I have two housekeeping books on hand - Home Comforts: The Art & Science of Keeping House (my book) and Martha Stewart's Homekeeping Handbook (borrowed from the library). To summarize: Home Comforts says to heed the label. Ms. Stewart advises that if the fabric is washable, launder it in the machine on the Gentle/Delicate cycle and hang to dry. She recommends ironing curtains while they are still damp.
I'm going for it since the curtains are plain white curtains and easily replaceable. As I type this up, said curtains are spinning ever so gently in cool water. Results of this experiment to be posted later…
UPDATE: Washing the curtains worked fine. There was no permanent damage done despite the label that said I had to dry clean them. In the future, I'll use starch while ironing. I'm very happy this worked as I'll be able to wash them more often and it won't cost me an estimated $75-$100 each time.