This is called the Blockchain. You can access it yourself if you use a client like the reference client, Bitcoin-QT. By reference, I mean that Bitcoin-QT downloads it to your disk... you have to write a program to access past transations, because Bitcoin-QT doesn't allow you to search past transactions other than your own.

Another way to access the blockchain is to use a web site like Blockchain.info. You can either use the web pages to review the blockchain, or use some of their APIs.