I'm a huge fan of emacs, but even though I use it constantly, I do not consider it exceptionally reliable. A modern experience really does rely on a huge number of powerful and excellent but sometimes glitchy packages. (helm, org, haskell-mode/python-mode/etc.) I also find it crash prone on Windows, which is not totally surprising given Emacs' ownership, but disappointing.
I've had emacs go out to lunch on rare occasions, but I find it to be far more stable than Firefox or Chrome. I have had emacsserver sessions run for months without issue, and I do all my email as well as coding and org-mode task tracking in Emacs.
I use Spacemacs on Windows so I'm pushing Emacs a bit past its limits. ;)
Actually I was going to compare Emacs stability to Chrome stability. Though for me Emacs gets terminal segfaults more often, Chrome has more random failures that require restarting.