I've used Libsyn to host two of my independent podcasts over the past year. My show and technical expertise has matured enough that it is now a better economic decision to host my show on my own server, but for many novice and experienced podcasters, hosting their own show is more trouble than it's worth. There are only a few podcast hosts out there that truly understand podcasting and Libsyn is one of them.
The sure mark of a host that doesn't understand podcasting is a host that has limits on either diskspace or bandwidth. Hosting your show with a host that limits either of these metrics means that you will eventually be penalized for being successful. A diskspace limitation means that sooner or later you're going to have to take some of your older shows 'off the air' and a bandwidth restriction means that as your show grows in popularity so will your bill for bandwidth. Neither is a desirable situation to be in.
Libsyn is one-stop shopping. They provide the space for your shows, a blog to put your show notes on, and a valid RSS feed for users to subscribe to your show with using a podcatcher. Further, Libsyn provides one of the holy grails of podcasters worldwide: decent listener statistics.
Libsyn has always proved to be a reliable host for my shows and they're constantly adding new features. They are a great place to start out and, for some, a great place to stay.