I'm a terrible Twitter-er (Tweeter?) mostly because I love having an empty e-mail inbox and, to me, Twitter is the complete antithesis of inbox zero. I'm also not interesting enough to warrant more than one 140 character update per week, really. I did some searching for the whole productivity and Twitter issue and came up with a few interesting articles.
Slate recently featured two somewhat conflicting, but informative, articles about Twitter and productivity. "Do I Really Have to Join Twitter" points out that Twitter is "not a faster or easier way of doing something you did in the past, unless you were one of those people who wrote short 'quips' on bathroom stalls." The second article, "What Are You Doing?," points out that Twitter can increase productivity levels, if only by allowing a "mental escape hatch" conveniently restricted to 140 characters.
And (thankgoodness) David Allen, master of getting things done, says that Twitter is okay, providing that you "stay very clear about what your agreements with yourself are, relative to your engagement."

Kazia: I agree that Twitter and inbox zero are pretty antithetical — which is why I found it almost laughable when one columnist suggested replacing email with Twitter. This is supposed to make life easier??