Well personally i don't use twitter but still i have seen 80% of the webmasters in several forums complaining that they are not getting traffic from twitter. I have also seen few gurus explain the method to get traffic 1) You should have at least 5000 followers. 2) You must not follow more then 10 people. 3) Give out lot of useful stuff free of cost to your followers. 4) Dont send unnecessary tweets to followers. Just send them tweets when you update your content or you find something useful. 5) Keep your followers under scan if you find any marketers troubling them then remove him. 6) If you see there isn't enough conversion then try to add people who are interested in that niche, you can do this by hunting on Social Networks like face book, orkut. There are few more, i think following some simple things like this might help.
But one thing is for sure most of the URL shortening sites especially bit.ly must be getting millions of traffic due to twitter.
Twitter does OK for me. It brings some traffic. However, it's not bringing in new traffic. It's basically the regular readers that are clicking the link from my Twitter profile.
Twitter as far as marketing is concern - It's a hype. Twitter Marketing is quite a tedious job for an individual to push on. Social Media Engineers nowadays are being employed among major SEO compaanies. They'll do the branding and get into the mix of the specific market that you are looking for.