1) Users can easily comment, with or without an account, with their Twitter, with their Facebook, etc.
2) It can create a greater amount of exposure for that particular post + comment (Through Twitter and Facebook broadcasts)
3) Disqus has a very clean look about it and the way it presents posts that I really enjoy
4) You can easily moderate + view statistics of various sites in one central location (Disqus website)
Hope that helps!
Not having disqus doesn't change my willingness to contribute, providing I can do so simply..like entering my name and email. If I have to register/confirm/activate forget about it unless it's a site I'm particularly invested in (say, HN).
From the development point of view, unless you have specific needs which disqus doesn't meet, I don't see why anyone wouldn't use them. They've turned the "writing a blog in language XYZ" tutorials into 5 minute exercises. On the top end, they are used by an ever growing and impressive list of people. Finally, since you can export all comments at any times, I really don't see what you lose.
I don't know, it's a bit too "in your face" if you know what I mean? A good UI goes out of your way, disqus doesn't quite do that very well.
That's just my opinion.
I actually use disqus for tumblr, because there isn't much of another choice there.
http://stackoverflow.com/questions/2500716/open-source-comme...
There are also lots of other discussions related to this on SO.
In my opinion: with disqus you get to be lazy. That's fine. I use it on my personal site. I don't think it allows for infinite branching (like on Reddit), but that requires a pretty nifty nosql solution, were you to do it on your own.
I used Intense Debate for my Wordpress blog. After some annoyances, I disabled it and switched back to Wordpress' own comments. I'll probably try out Disqus when I have time... It will irk visitors, but you can switch between commenting systems if you want to test.