Mails. Years of mails

I got my first e-mail account – thanks to hotmail – I think in 1996. Since then I have written/received thousands of mails. If you take the case of my fiance and I, e-mail is the only way to communicate, given we live in different towns. E-mail has been (and still is) the bridge that brought us closer. So I had this idea, why not compile a chronologically sorted e-mail ‘book’? Obviously it is private and I won’t share it with anyone else… but still, isn’t it a great idea? That brought the question, ‘Is there a way through which I can extract all my mails from my inbox and save it on my computer or something?’ (that was my fiance asking the question, I am well aware of ‘archive’ on my Lotus Notes and Outlook, but the question has relevance if one has only free webmail accounts).