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.
You can use Gmail filters to label these messages, and set the notifications to only be for specific labels.
I think most mail clients (like Touchdown, and the default mailclient, etc) do not have support for sophisticated notification schemes like you want. I suggest disabling your mail-reading app's notifications and trying a separate email notification app.
Poking around the market I found this app:
https://market.android.com/details?id=com.willdev.mailalert
and this app:
https://market.android.com/details?id=com.netcompss.efilter
I have not tried either of these apps, but the descriptions seem a reasonable match for your problem.
I searched the market for 'email notification' and 'email filter' (the search returned a lot of irrelevant stuff, so there may be other useful apps buried in the results)....
I just needed to do this and it was fairly easy using this method:
Install IFTTT (free app that supports all kinds of awesome rules).
Create a new "applet" where:
IF This: checks gmail for messages according to whatever criteria you want
Then That: send notification
I'm doing this to try to get exchange messages from work (but cannot access or send content outside of work). I wound up creating a rule in outlook that sends a new message to my gmail account with a set subject/body (via a script). IFTTT searches for new messages with that subject and pops up a notification.
I used this page to help me create the script to create a new message: http://www.slipstick.com/outlook/rules/send-a-new-message-when-a-message-arrives/
I saw that you don't trust Google with your personal mail. The gmail account you use could be a dummy account (I assume you may already do this since you're on android). Or you could use an alternative trigger from IFTTT.
If you don't mind paying money check out touchdown. There is a free trial but I think it will do what you want.
