I've turned that off, because I tend to get notifications in my clients. There's no good Windows client yet though, so when I'm on my gaming machine and don't have my phone handy, I use the web client for tweeting, and I never notice DMs.
I like Echofon a lot. Their Windows client is essentially just their firefox plugin running as it's own app, but it's pretty good.
I especially like that I can sync all the tweets I've read between my Windows machine at work, my iPhone, and my Mac at home. I don't know of any other app that works for those 3 platforms and has syncing.
I'll give that a try, but I don't care much for Echofon on any other platforms.
There is a service called Tweetmarker (http://tweetmarker.net) which some clients are now using to flag your last-read location amongst other clients on other platforms (e.g. Osfoora on Mac and Tweetbot on iOS).
I figure out they have 2 designers there, one really good and one that doesn't have the slightest idea of UX and design
Case in point: the way DMs are notified to the user. That's right, in the previous web version it wasn't. And this version is better, but not great