It is said that there is an improv practice of "yes, and" - where you eliminate "no" and "but" from the flow of a story because these things shut down the fun. Some people have taken this into their lives with the intention of seeing where it will lead them - open eyes and wondering at the world. Jim Carrey even made Yes Man around the idea.
But there is obviously another take to this. When I don't take control of those requests, I can become slave to every interruption (or request every request that comes through on my calendar). Poppy Harlow (CNN anchor) had a great piece in yesterday's USA Today on Finding Happiness in 'No', where she described her journey in learning how to set limits.
In my personal and project world, there is a big benefit to being able to say "no" or "not now" to requests that come across my desk (or that pop up on IM). I am trying to live in a world where I prioritize FINISHING over being responsive. It's so much easier to respond (immediately) to everything, when in reality it is much more rewarding to actually get things done.