I don't know anything about Linkedin (never even heard of it), but the big thing with Twitter, blogs, facebook, myspace, etc. is just that those are the means through which most people expect to get their information through nowadays. They are cheap (if not free), easy to create, easy to manage, and a good way to reach a large number of people.
I've tried Twitter and didn't like it, but I think the big thing is that it just helps a fanbase feel more connected with an artist. I can't say I'm one of them...but a lot of people go nuts over arbitrary information such as "lol zomg I"m eating a good sandwich right now". I find that particular site to be rather useless for anything substantial.
Blogs are good because they are a good way to generate interest in you/your product and draw traffic to yourself. Blogging about things and then including relevant links is a good way to draw hits from search engines, which will in turn lead more people to you. It's a good way to network.
Myspace is the big one for artists just because it's become the standard for EPKs. Photos, video, calendar, audio, biographical info, contact info, etc. all on a single page that it easy to access and easy to track. The account services for artists are good as well...it makes it very easy to track who is checking you out, where they are from, how often you are getting people to the site, etc.
Facebook, I see as more of just a networking thing. I use that one for personal use (any other social networking tool i use/have used has only been for professional purposes), but find it very good for professional networking as well. I've got several stories about how I've gotten gigs and other work through seemingly arbitrary internet-networking, including a tour of Europe for next year. It's also a good way of keeping current with friends I don't get to talk to in person as much anymore (I've moved a lot and have friends all over) and keeping friends updated on what I'm up to as far as gigs and stuff go.
All in all, I'm really not a fan of most of these things, but they are a necessity in this business nowadays. It's all part of this "fast-food" generation.
EDIT: I guess my responses are only in regards to the benefits for MY profession rather than generalized things...but I think some of it holds true across the board.
