I decided to try the winter rye as a cover crop for a few different reasons. As you mentioned, it competes with weeds and protects the soil over the winter. Also, from what I've read it adds nutrients and improves the soil's structure while it's growing and after it's turned under. My dad, who is a large-scale farmer, gets a kick out of seeing my miniature urban rye crop. I think it looks nicer and more "occupied" than bare ground, too, which I'm more concerned about since I'm renting and the plot is pretty visible.
I read about cover crops, also called green manure, in The New Victory Garden and the New Organic Grower.