I have all notifications turned off on my mobile devices, except for calls and SMS.
I use the same strategy for my computers as well.
If you send me a message or email I will eventually look it up and respond at appropriate time. If world is ending and someone needs urgent help they will call me.
Call me too many times and I'll put you on mute. I'll still get the notification but you'll have to wait till I have time to call you back, or more probable, I'll wait until you send me a text message stating your need.
One thing I hate the most is people calling on repeat. I'm old enough to remember times before mobiles and back then it had a purpose. Now it doesn't. If you call me once and I didn't picked it up that means I'm either busy or away. If you call again you're just annoying and I'll flag you as such.
One thing that may set me apart is that I still consider my phone to be just that. I lived the whole mobile revolution and from time to time I've tried installing different apps, but eventually the phone for me is just that - the phone. Calling and messaging. Sure I can browse, use maps, etc. but it's a communication device.
And when I don't want to communicate I just put it away. Problem solved.
[EDIT] Yes, you can still send me an email or a message through a messenger application, but unless I intentionally check the app I won't even know you're there.