Twitter CEO Dick Costolo has confirmed that they eventually aim to provide an export tool to all their members to allow them to export their entire database of tweets.
We expect third party tools to accept this file to allow users to conduct a variety of actions on them including search.
Twitter is also working on a feature that would allow users to search through their own tweet database. However, the company does not plan to provide a search function that provide results from the entire Twitter archive.
Twitter sells access to their entire tweets database to third party services that provide similar functionality to paying subscribers.