This post is out of date and kept here as an archive. See instead A list of tools for finding or capturing tweets (30 May 2011) - ironically it too is getting out of date ;)
The text below goes into some depth for a handful of tools but the 'list of tools' linked above covers a greater breadth but in less depth.
What The Hashtag (taken over by What The Trend) is now providing some sort of coding information for people who know how to do something or other with JSON (evidently not me) and anyone who knows programming and apps and stuff can probably get create their own system. It's the same URL (http://wthashtag.com/) but it's now What the Trend API.
Edit: 14 April 2011
Edit: 6 June 2010
Another service that I've yet to investigate fully is the search engine Twoogel (http://twoogel.com/) it uses Google functionality (eg inurl: or site: ) but I've tried it and it's not picking up much individual stuff at the moment (36 tweets of mine, out of about 9,000) but it picked up over 100 tweets from the Science Communication Conference when I searched for it by hashtag #scc2010).
Of course if I'd done better research I'd have saved myself writing this as Loic Le Meur has already written what is probably the definitive post, and it's likelier to attract more comments and new suggestions so recommend visiting it:
Tools to back up your tweets
I've not included any information on tools that will save your tweets for you (you can use Twapperkeeper for this http://twapperkeeper.com/index.php though it goes only as far as 2009, and there are other tools).
Twitter's own search engine is well known for being a bit useless in finding old tweets - 'Old tweets are temporarily unavailable' being a typical response when looking for something. Edit: Twitter's search has got better (2011) but still goes back only a few days. Services like Chirpstory or Storify can go a bit further back in time than Twitter.
I use FriendFeed to search my previous tweets - they are all there, eg http://twitter.com/JoBrodie/statuses/2236469325 - from June 19 2009, but you can't hack that Twitter URL (ie tweak the numeric part from 2, 236,469,325 to 2,236,469,324 etc) to find older tweets.
This is a real shame - you used to be able to do something similar before they brought in the 'More' button that appears at the bottom of the page. It used to read 'older' and it allowed you to go backwards through pages of tweets, but each page had its own URL (doesn't now) and so you could easily amend the URL to go from page 200 to page 1 very quickly. The new 'More' system just refreshes the page with another 20 previous tweets, but the URL doesn't change, meaning it's much harder to interact with it.
You can tweak the 'More' button URL a tiny bit, but it doesn't go all the way back to your Tweet Zero.
Go to your own Twitter profile, mine's http://twitter.com/JoBrodie and then scroll to the bottom of your page. Hover over 'More' and note the URL that appears in the status bar at the bottom of the window (if you don't have status bar on, make sure it's ticked in the View or View > Toolbar menu).
However, we've already seen that Twitter still has all the older tweets, but that they're largely inaccessible at the moment... on to FriendFeed.
Importing your tweets into FriendFeed and using their search
I've always used FriendFeed if I ever want to find any of my old tweets (I've found my first tweet http://twitter.com/JoBrodie/statuses/841825864) by using their much more powerful search engine. This does rely on having a FriendFeed account (I recommend this) and also on remembering keywords you've used in your tweets, so that you can use them as search words.
You can search other people's tweets too either by subscribing to their FriendFeed account, if they have one. If they don't have an account, but their Twitter feed isn't locked, then you can still use FriendFeed - you need to create an 'imaginary friend' account for them and import their twitter feed to that. I've previously written a how to blog on this:
Cunning use of FriendFeed - find old tweets, yours or others
Sometimes though you might want to find out what has been said on a topic without knowing exactly the words that may have been used. It looks like Google might be on the case with this, as it rolled out (in April, I'm just catching up) a searchable archive of Twitter. At the moment it only goes as far as February 2010 but according to Google's blog their intention is for it to go back to Day One of Twitter, in 2006.
2. The search results, after pressing enter, are shown below... click on 'More', highlighted in the picture below with a purple oval.
Keywords - I've put them here because Blogger refuses to update this post with all the ampersands in the keywords. I can't see what ampersands it's talking about to be honest but I've given up fighting with Blogger's ridiculous formatting demands. One day someone will work out how to make a blogging platform manage text (and no, it's not WordPress either I'm afraid, if anything it's worse).
"how to", "twitter tips", archived tweets, finding old tweets, how to find old tweets, tweet history, twitter archive