You do not need a broadband connection. IF you have one however, the benefits would be:
1: You can log into your dvr remotely through Dish's web portal, and schedule a future recording. Comes in handy if you are working a shift, and find out about something you'd like to record. I did this myself just the other night, when I found out about the "Finding Atlantis" program that was starting in an hour.
2: VOD, which on Dish is DEADLY slow, because it downloads to your receiver before playing. On my 3Mbps line, it can take 24 hours for an SD movie to download. Also: once you start it, it's impossible to cancel, until it's completely downloaded.
That's about it, I think. Oh, I think there's some games and such on channel 100, but I don't play those, so I'm not sure if you need broadband to do them.
Though, what used to be an additional advantage, was they wouldn't charge that monthly fee for not having it connected to your phone line. Some people had broadband, but not a usable phone line to connect to. They no longer charge for this, so it's not an advantage anymore.