Update: Twitter changed their API in March 2013, so this doesn’t actually work anymore. I’ll update this page as soon as I find a solution.
The other day I was trying to figure out how long a particular Twitter account had been around. It doesn't say so in a Twitter profile, and while there were a lot of tools to do this, none of them worked. Turns out the information is available from Twitter, you just have to pull up an XML file to find out.
Point your browser to http://twitter.com/users/show/USERNAME (in my case, http://twitter.com/users/show/alexinfact). A few lines down, look for the <created_at> tag. The string that follows is the exact date and time that the account was first set up.
I've tried this with a handful of accounts that I know the creation date for, and it appears to be accurate. If it's not, or of you know a better way, the comments are below.