I used to work remotely and had my own hardware, etc. The company used Microsoft exchange (or similar) to run their email, store it on servers, etc. They killed my email account when I left but all my emails still remain on my laptop. Do they have a right to compel me to destroy the emails on my computer? Do I have a legal right to keep them?
Do they have a right to compel me to destroy the emails on my computer?
They have the right to apply for a court order to get you destroy the emails. But this would hardly ever be granted unless the emails contain data affecting national security (in which case you won't legally have it on your own hardware in the first place).
Do I have a legal right to keep them?
You do, provided that a court has not said otherwise. You cannot, however, use them for anything but your own reminiscing of the time you worked for the company, or as evidence should you decide to sue them (or be sued by them).
You also may become liable should the emails leak from your hardware (e.g. stolen by a hacker, or accidentally uploaded to a cloud storage and made available to others).