I did something the other day that was done kind of out of an angry place, but has really made me happy in the long run. A week ago I turned off the auto-email check on my phone, and I don't miss it at all. Now I check in on my email when I feel like it, instead of being alerted at random moments of my day to emails that I largely do not care about.
I won't ever take the email app off of my phone, because there are days that I don't sit down at a computer and some of these emails do need a response. I don't think that I'll ever go back to pushed email notifications though. Even just the way that it's worded bugs me now. I don't want the phone to push my email to me, it can fetch it for me when I am ready to see it.
That's pretty much the approach I have with all the various apps and things now. I don't even like it to give me little number badges over an icon to pester me into looking at it. If I feel like checking on it I will, until then it should just sit there and be quiet.
The exception I make is for actual phone calls. It is a phone after all. So my phone is allowed to let me know when people call, but that is all.