I had a problem when an ISP with free email accounts (akin to Hotmail and GMail) suddenly decided to remove the accounts of those access the free versions. I lost all my emails AND access to my email addresses. I had problems getting access to a number of sites (SQL Server Central being one - thanks Steve for sorting that one out!!!) and people still are trying to contact me via those email addresses as occasionally gets mentioned on phone calls.

I purchased my own domain to resolve that. I store a copy of all emails locally and they are hosted by a mail service as well. Worst case scenario is that I lose a few emails or email addresses (if I haven't updated my records).