The usual ones are RoundCube and SnappyMail (which is a fork of deprecated RainLoop). I’m hosting SnappyMail to access my Dovecot when no other mail client is handy.

How does it compare to Adminer?

UberSpace. Managed hosts, but you get SSH access and they have a manual for the basics as well as user-contributed guides for specifics.

It’s ran by nerds and the only limit is your allotted disk space (10GB by default). Unlimited email accounts, unlimited aliases, etc.

“Pay what you can afford” model starting at 5€/month.