Topsy is a social media analytics company that has just built a Twitter-based search engine that has every tweet ever written indexed in their system, starting with the very first tweet written by Jack Dorsey in 2006. Topsy is offering the ability to search the index for free.
You may expect that Twitter and Google may be doing a good enough job indexing the tweets, but that’s not trust. Twitter shows around 7 days worth of tweets when searching for content. Google’s indexing of Twitter ended in around 2011 when their agreement expired.
Topsy’s index only covers public tweets so don’t worry about your direct messages and protected tweets from being found.