How do I make it stop?
You probably have a subscription that has been set to "auto-download". First, find out which subscription (or subscriptions) is involved. You can do this in one of two ways: Click on the Grey subscription button in My Library for one of the mysterious new downloads and look under "Related Subscriptions"; or look through your subscriptions to see with have "Auto-Download" (a check-box in the upper right of the subscription page) selected. You can deselect it, so Vuze will only download new items for that subscription when you select them for download. Or you can check for a subscription that selects content more narrowly so that it doesn't find more content than you -- or your hard drive -- are prepared for.