As this article on Twitter Growth on TechCrunch shows, according to ComScore in the month of may Twitter has surpassed the web visits of Digg, LinkedIn, and NYTimes.com. ComScore estimates Twitter at 32 million global visitors, which is impressive considering how many people use the service with a multitude of clients (including phones) and don't use the web site itself. This is the ComScore graph: 

Checking out on Alexa top site ranking, Twitter holds the 37th place as of today, but half of the places above it are taken by various Google properties (including national Google landing pages). Alexa rates Twitter at a 280% increase over the last 3 months: