Cochlear brand cochlear implants do have on/off switches. My early model, the one I got in 1997 and still use because the later models suck ass in terms of sound quality - sounds like they're not sampling fast enough; it's robotic, even after lots of tweaking - has a mode that attenuates constant noises such as road noise, loud conversations in crowded rooms, etc, but it's not that good. In those cases, I plug in an external mic that I give to the person to whom I want to listen, often my wife, so the sound is picked up mostly from a discrete point. It helps greatly.
On the other hand, and this will address MikeBabcock, below, as well, there are times when I take off my CI - like when exercising, where sweat might short things out, or sleeping, where it gets in the way - but I'm at the mercy of whatever I can see or feel, which is risky. In the event of a fire, I'd be toasted, if my wife was out of town and I was by myself. Sure, there are alarms that flash brightly, but I don't have those; I kind-of depend on my wife for that. I probably should get some. My alarm watch buzzes, which is great to tell me when it's time to get up, but not useful in terms of fire protection or intruder detection. When riding my bike, I don't hear cars coming from behind. I've had a few close calls, but have never been hit, fortunately. I have lost my grown son off the back and had to turn around to find him with a flat about a quarter mile back, which sucked. So, in general, unless I have to take it off, I wear it. Sometimes, like on an airplane, I'll just turn it down, or plug in my iPod, which cuts out everything else but my music. In department meetings, I'd plug in and no one would know I wasn't paying attention to the PHB, unless I was obviously jammin' away. That was an enjoyable bonus. Except for those times when people would talk to me, and I didn't even know it until they tapped me. Oops.