There are several threads on Apple's discussion boards covering the issue, and most seem to converge on the suggestion that a large download queue may be behind the problem, or a single corrupt song that blocks further downloads. If doing a manual check for purchased and undownloaded music doesn't solve the problem, Apple's download support page for iTunes recommends submitting a problem ticket within your iTunes purchase history; this should allow the customer service agent to clean your queue and improve your download experience. For worldwide customers, the main directory for iTunes support is here.
For what it's worth, late Wednesday night I bought an album that downloaded cleanly and quickly, but obviously people's mileage is varying. With the level of attention brought to the iTunes store by the NBC withdrawal and the iPod product announcements, this is not the time for Apple's technical execution to falter; the iTunes Store didn't get to be the #3 music retailer in the USA by stalling customers in the checkout lines. We'll keep an eye on the trouble reports and see how things progress.
P.S. One year ago, the iTunes store was down for a good reason...
Thanks to everyone who sent this in.