Pete Freitag solved the problem with Solosub. You simply enter the URL of your RSS feed on Solosub.com. The tool then gives you the link to publish on your blog. When users click that link, they will be invited to select which RSS reader they want your RSS feed to be sent to. The user can choose to have Solosub remember that choice, and, from then on, the user will just click on any RSS feed that uses Solosub and suddenly be subscribed to that feed via their reader of choice.
Nicely done, Pete.
Here is my feed:
Update: Micah Laaker reminded me that there is another rather elegant solution for this from Jason Brome called "quicksub". I've seen this elsewhere, and it's nice because I may want to subscribe to a certain feed with one type of reader and another feed with a different reader. There's a clutter problem here, but it's definitely better than having stacks of RSS chiclets on your blog.