In what they have said is their #1 request (it certainly was mine!), Evernote has added reminders.
You can specify a reminder date for a note, and Evernote will email you with a reminder for the note. The reminder also pops up in the app.
Right now, it works on IOS and Web, but the other clients should be getting it very soon. I hope it is sooner than Reminders itself. Phil Libin said in one of their podcasts that Due Dates were coming "soon". That was at least two years ago, maybe three. Supposing Reminders are what he meant as Due Dates, he has a rather loose definition of soon.
Joking aside, this is an awesome feature addition.
Also the notes with Reminders end up at the top of each Notebook, and you can arrange them by your order of importance.