Robin Barooah gradually weaned himself off coffee and found that his concentration actually improved. He explains how he did it and what he discovered on the Quantified Self blog, which covers news about self-testing and self-monitoring.
As part of a separate experiment, I have been keeping track of the amount of time I spend working on projects. I work in 25 minute intervals which I time with a coffee timer, and I mark an X in a paper journal for each interval that I successfully complete. If I get distracted, I don't mark the X, and if I can't concentrate, I abandon it and don't mark an X rather than sitting out the timer. I've been doing this since the end of June, so I tabulated the data and created a graph of my hours of concentration per day, and overlaid a bar showing when I drank my last coffee.
Causality is a complex issue. Obviously this is an n=1 experiment and I am intentionally doing other things that may well be improving my concentration, but one thing is very clear; the amount of time I spend concentrating has not deteriorated since I quit coffee, so I can easily reject the hypothesis "I need coffee to help me concentrate."