Instead of reading or replying to things as soon as they come in, I just silence everything on my phone except phone calls. That way, I check emails, texts, tweets, etc. at my convenience. It interrupts me only when necessary.
I don't even answer phone calls. Why is some telemarketer calling me more important than my friend saying something on Twitter?
Sure. I just don't get many unsolicited calls.
I keep SMS and phone calls making noise, but don't often answer them unless I'm out and idle. I just note that I have something to look at when I get back to my desk.