There are several potential problems associated with using a free email address at the time you register your domain name. First, the service may close down without warning (indeed, hundreds of free email services have closed in the last year due to the weak internet advertising market) - this will leave you stranded when it comes to making changes to the domain name or transferring it to another Registrar, since you will no longer be able to receive - and respond to - email confirmations. You'll also liable to not receive reminder emails telling you that your domain name is about to expire.
Secondly, as public services used by thousands or millions of people, free email services are generally more susceptible to being hacked. If a hacker were able to get into your email account, he/she might be able to make changes to your domain name record without your knowledge or permission.
Finally, some free email services delete inactive accounts after a certain number of days or weeks. If you go on an extended vacation away from your email, or for some other reason forget to log in for a few months, you may find that your email address has been deleted and re-allocated to somebody else, giving them FULL control over your domain name!
We do not recommend that you use a free email service as your listed contact address because of these problems, although you most certainly can use these services at your own risk.