So how do you get to your old tweets?
Head to the Settings menu on Twitter.com and at the bottom you will see a button to "Request your archive." Click on that and Twitter will then email you with the instructions on how to download your archive.
When you download the file sent by Twitter you will be able to open the file in your web browser and view your tweets and even share them. It's an offline file, but you can view it in your browser and even view the Tweet on Twitter. You can't retweet your own tweets since Twitter doesn't actually let you retweet yourself.
Twitter has also organized your tweets by year and then month. You can hover over the months and see how many times you tweeted at a specific time over the last few years.
Twitter says this feature will begin rolling out to everyone today -- if you don't have it just yet, it's on the way. Just get ready to sift through a few more tweets soon.