@BenLunt I tested this right now and e-mail service is working. I’m getting every requested e-mail (incl. droplet creation info and reset root password).
I recommend you to try again, and please check your Spam folder if it is missing in your inbox.
If this doesn’t help, contact support and they will be happy to assist you.

I recommend you to use SSH (also called public) keys. Problem is after droplet is created you have to login and config it to use SSH. This tutorial covers it.
If you create new droplet, on droplet creation page you will have option to chose SSH key, so you can from creation login with that key, and you don’t wait for root password to be mailed.
Before you can use SSH key on droplet creation, you should add it under your DO settings.
Go to Security settings-SSH keys, click on Add SSH key and copy id_rsa.pub content to SSH key box. You can give any name there. After that, SSH key will be shown on Droplet creation page.

Also there was some DO Control Panel and API problems which could be reason your emails are missing. It is resolved now as said on Status page. Anyways, as I said, if it still not working, support will be happy to assist you. :)

Use public keys instead of passwords and e-mail support@digitalocean.com to fix the email issue.

how do i use a public key instead?

I can’t log into my new droplet because I’ve been sent the password in an email that i have not received.

Ok

I’m running into the same problem. I wonder if it is due to custom dns forwarding from my registrar to DigitalOcean.

My email doesn’t appear to work at all, I don’t even receive emails from myself anymore. I’m no domain expert but assistance would be incredible.