I don't think I'll ever remove the brakes, but I have noticed that after riding for a few miles, my instinct to slow down has been to resist the forward motion of the pedals instead of pulling the brake lever. It might get to a point where I don't use the brakes, but I don't think I'll take them off...mainly because I might want to use it as a single speed.
While riding, I found myself reaching for phantom shifters to change gears. Maybe that habit will disappear over time. I think that I shift more than most people on geared bikes. Not being able to drop gears makes me have to recruit more power from my legs when climbing...which I hope will turn me into a better climber when I can switch gears.
I had to take off the stock pedals. I put on Power Grips instead because I wasn't getting much power out of the upstroke on those plastic toe clips. I hate toe clips anyway...but the ones without the straps aren't as bad.
If anyone's thinking about switching to riding fixed, I would offer the following advice: wear a helmet and equip your bike with 2 brakes. You don't have to use them, but you might want to have the option. At least use a front brake because you can stop way faster if you use a front brake in conjunction with a skid stop (I haven't been able to get a good skid stop in yet...but physics will tell you that my previous statement is true).