Email application with notifications only for specified contacts (standard SMTP/POP3/IMAP) I have a lot of mail traffic on my phone. But I want to be notified only for mail from certain contacts like my family, colleagues/boss, critical automated systems or at least any contact in my phone contact list (with email typed in).

Are there such applications which can access email on my personal/corporate server? Standard IMAP (or at least POP3) + SMTP, not some proprietary protocols like Exchange/Gmail.
I haven't found a standalone app but K9 in conjunction with WhoIsIt Lite supports this. It doesn't do away with visual notifications mind you, but it can silence them.

Alternatively you could investigate whether your workplace email support server based rules. You could use them to filter unimportant emails into a folder other than your inbox. Android's stock email app only checks for new emails in your inbox so the app would ignore the others.