Here's a snapshot of Twitter's traffic over the last 6 months, via Alexa:
The spike in mid-March occurred when Twitter blew up at SXSW.
But look at the site's traffic over the last 3 months:
Appears that traffic to the site is leveling off. I think by now, most people that are going to pick up on the site have started using it. I'm seeing almost no Twitter talk on the blogs I frequent, after being inundated with talk about the service a couple of months ago.
I think it will be interesting to see what this graph looks like in a couple of months. Personally, I just never have gotten into Twitter, but I know that many enjoy the service. I think the problem for marketers is finding a way to filter all the messages left via Twitter, based on relevance. I haven't used Twitter much, but I haven't read about any way to search the messages left via Twitter. If Twitter adds this functionality, or if someone creates a widget that does this, that could boost usage significantly.
As I said, I think the next few months will tell the tale for Twitter.
UPDATE: Scoble takes credit for Twitter's growth.