Personally I trust Fastmail to stay. They are 25 years old and are still in their growing phase. They don't rush anywhere: they build their service slowly.
I'm quite sure Gmail is here to stay: that is unless Google will come up with something that can replace email and they can make it happen (unlike
Google Wave). If anyone can make something like this happen, it's only Google, and if they can they will, don't believe this can happen in my lifetime.
Hotmail (and it's various synonyms such as MSN, Live, Outlook etc.) is here to stay as long as people use email. I don't believe that Microsoft will be the one to replace email by something else.
Apple mail probably also is here to stay, and Apple will not be the one to replace email since they are a closed network.
Another one I use and I forgot to mention: Spamgourmet: it almost died with the person operating it, and it was saved by someone who volunteered to keep it going, and I don;t think it would go away any time soon, and when the comes another volunteer will take it.
If you mean which one of my email accounts would outlive me: I guess my own domain. My kids are also using it for their main accounts, and they would keep it going.