Hotmail is the most popular
free e-mail service, but I don't think it's the best.
I tried Hotmail and it was horribly painfully slow and annoying to use.
I've had no problems at all with Yahoo Mail and it is what I would recommend to you.
I have a Google Gmail account, but Gmail is kind of annoying in comparison to Yahoo Mail. And with Yahoo Mail, you don't need an invitation.