@loridr - some changes were made recently so that anyone with a wordpress or gravatar account has to log in. A lot of non-wordpress.com bloggers have gravatar accounts so that their image and profile can show up in comments in other blogs. If someone who's trying to comment in your blog has or even once had but not longer uses, a gravatar or wordpress account then it will be linked to the associated email address. They can either log in via the account - or reset the password if they've lost it, and Timethief's second link gives that information, I'll give it again so you'll know which one I mean:
Or an alternative (but then the commenter won't be able to receive comment notifications) is ask your commenters to add an x or some other character to their email address so that it's not recognised as one attached to a gravatar or wp.com account.
You can change 'leave a reply' message (or whatever it is for your theme) near the bottom of the discussions settings on your dashboard, so that people will know what to do, if that helps. (It probably doesn't but it's just one way to inform people.
All this is a pain, and I sympathise - most of us here in the forum answering questions are just volunteers and we can't change any of this, only staff can and they won't!