For something as important as email, I’ve never trusted everything to a proprietary provider. My email address has never ended in someone else’s domain name, and has never been hosted in any way that would preclude me from easily switching to another provider.
I can’t exactly say I’ve followed this practice; for the first few years of my Internet existence I had a hotmail account, and I still have a gmail account, though I don’t really use it. But I have since early 2003 essentially controlled the domain name that my email address has been on. (I say controlled, because you never really own a domain name; it’s merely a glorified rent system, but that’s beyond the scope of this writing.)
Aside from the obvious benefit that one can usually land an address that’s infinitely better than what one can get at Gmail (or Windows Live or whatever), it gives one the possibility of switching hosting providers, without people contacting me knowing. I have done so, as of this writing, on three occasions, and I have never had to send out a mass-email telling that my address has changed.
Sometimes people get an email address from their ISP, which is even worse, because while Gmail deciding to close their doors might not be highly probable, your switching ISP probably isn’t a foreign concept.
Likewise, if the only email address you give out is your work email, not only are you mixing the types of messages you get there, which your employer might not appreciate, but when your employment eventually ends, people can’t contact you anymore.
One very basic piece of advice that everyone really should follow: register your name as a domain, and get email hosting for it. I use WebFaction (affiliate link), and like them, but they might not be for you, or too expensive, or what have you. But get a domain that you control, and worry about the rest afterwards; you can always change providers, that’s the beauty of it.