I am using Twitter for traffic purpose not for link building.
Twitter is a social networking site and give good traffic for my site.
Twitter can be a great way to engage with and communicate with the audience that you have already built up but I don't see it as very useful for building up links or promoting new traffic. I have the "Retweet" button on my blog and I got some traffic from it but not nearly enough to justify a dedicated Twitter effort.
Consider them like a referral when business networking. NoFollows don't assist much organically, but do for people in the market looking or curious.
Google now uses a new type of search index they developed called Caffeine. It is faster with submissions to the index and near realtime. If you do a search on relevent current events, you'll often notice, in the organic listings, Twitter posts within it that are from that day.
Yes Twitter is organically as good as it gets now and is very important.
http://identi.ca/ is a good one for helping you get indexed on Google fast. You have to post your proper url and not your bit.ly url to get the back link.
Twitter is for sure the most popular micro-blogging service which you can use completely for free on the internet. Allowing you to post “short” status updates anytime, anywhere you go and you are.