In 2006, Twitter and its related lexicon had not yet crept into the global consciousness, but the site was home to a variety of early adopters and businesses looking to expand their social networks. The tweets written then are mostly still around, but you're not likely to come across them. Coder Kellan Elliott-McCrea, though, wanted to make it easier to explore these early messages, so he created Oldtweets, a search box that limits you to seeing tweets with an ID from the first year (for the curious, that's apparently a range from 1 to 20 million.) You can limit the tweets by account, but it's more fun to enter a term and let the gestalt of fledgling Twitter wash over you.
Update: New picture added.