Even easier: I have a list of pre-generated fantasy addresses on my smartphone and can pass one to randoburgerspot on the fly.
Highly unrecommended if it's important or you're a repeat customer. It is easiest to pick a consistent generation scheme that helps you to remember the email address you gave. Obviously record it somewhere too (a folder for the first you've-just-signed-up email is easy)
For throwaway accounts it doesn't matter what you give.
If I could think of an unambiguous .com, .net, or .org that is a pronounceable word that wasn't registered already by 2001, I'd be maybe willing to try this again.
Not to mention that I've been told by a couple people that they find it to be an awkward email address. Sending to "me" from their perspective should mean sending to themselves.
I keep expecting to have to explain, but the vast majority of the time people don’t ask.
(only half joking)