Twitter may be a great way to keep up with what's happening, but it's not so good at keeping track of what's happened. That's because Twitter itself offers no way to keep an archive of your tweets.
It's true that you can search your own postings (from your Twitter page). But those searches are limited to the last 3,200 tweets you have made. And if you want to store your tweets for posterity, there's no built-in way to do so.
Fortunately, there are some third party tools and services that can archive Twitter for you. These third parties describe what they do in different terms: Some call them "archives" and others "backups." Some save everything, others let you perform searches then save the results. But all of them allow you to collect your tweets in a file or web page for later access. Here are a few of the most notable Twitter archive tools.
Use your iPad
If you have an iPad, you can use Tweet Library, a Twitter client that can also archive your tweets. When you first launch the program, you can start downloading up to 3,200 tweets by tapping on Archive. Then, as you continue using Twitter, Tweet Library will add your new tweets to the Archive. You can filter your tweets and make "collections," groups of tweets you manually collate.
It will also export those archives in a variety of formats for later viewing. You can do so in two ways: You can send an email, containing the raw tweets with dates and times or you can export a .CSV file. Because you can import the latter into spreadsheets or database programs, that latter option could be useful if you manage social media for a living.
In either case, you get a record including the tweet's text, any included links, the date and time it appeared and its URL.
On the web
There are a number of web-based services that let you archive your tweets by searching past posts, maintaining ongoing archives or both.
The free version of Twistory will show you your last 30 days worth of tweets. For $1 a month, it will show you all of them, up to Twitter's own 3,200 post limit.
What makes it unique is that will also show you those tweets in an iCal or (experimentally for now) Google calendar. Doing so is simple, just click the appropriate button on your twitstory profile page. If you select iCal, you'll switch to that app and be asked if you want to subscribe to a new calendar. The site says it updates several times a day, your iCal calendar will update accordingly.
The free Tweetake will collect a backup copy of your tweets (up to that 3,200), tweets by friends and followers (up to 10,000), favourites and direct messages (200 and 1,000 respectively) or all of the above. Whichever dataset you choose, you'll download a CSV file containing all of the available information. But Tweetake doesn't maintain an archive for you, it's an on-demand service only. So if you want to use it, you'll need to remember to run new backups from time to time.
The Archivist offers a free tweet archive service, structured around searches. First you do a search using Twitter's own search syntax (from:yourusername, for example). It will then return a list of matching tweets, along with a slew of analytics (volume, word frequency and so on). Your first search will return a maximum of 500 matching tweets. You can then save that search (which will continue to be updated until you delete it) or share it.
If you're really geeky type, you might want to store an archive of your tweets on your own server. TwapperKeeper is an open source PHP/MySQL-based system that automatically grabs all your tweets and copies them to a database on your server, which you can theny view, sort and search them on a web page. This page updates continuously as you tweet.
Finally, if you want to save more than just your tweets, backupify lets you back up all of your social media accounts: Twitter, Facebook, Picasa, Gmail, as well as others. A free account has a limit of 1 GB of storage. If you just want to archive your tweets, at 140 characters each, that should last your lifetime. Paid accounts offer more storage and more frequent backups.
One note: if you try out any of these services, you'll need to authorise them to access your Twitter account. You can always deauthorise them, or any other services you no longer use, from Twitter's Connections page.