I use email on my iPhone / iPad as a secondary device, when my computer is turned off. I have email accounts for personal use and work. My work account can be used with IMAP and/or POP3 so it works reasonably well. However, my personal account only allows POP3 and it is a mess on the iphone and ipad. I need the following mail management options:
The phone should read email and leave it on the server.
When I delete an email from the inbox I want it deleted from the server.
When my computer reads the email and takes it off the server it should be removed from my phone automatically.
When I send or reply to an email I should automatically get a copy.

The iphone email client almost does this if I use IMAP on the iphone and POP on the computer, it just doesn't allow me to have it delete email from the server when I delete it from the phone.

When I use POP on the iphone it reads the mail and leaves it on the server but there is no option to have it delete the mail from the iphone when the mail is removed from the server.

There is an app called K9Mail for droid that does this.