I once rode without a bell but now I cannot imagine doing so. It is important for me now because I ride around a large number of pedestrians. The bike I ride the most has flat bars and thumb shifters. The bell I use is one of the Electra bells that looks like this.
I have seen some unique bell positions on bikes over the years. I have seen a bell rigged up to be used with a piece of string and oddly saw a bell on a seat post once. When it comes to mounting, not every bell is suitable out of the box and reader Yuval informed us of an instructable, or instructabell, he came up with. The end result looks like this.
The full instructable, found here, goes over how he upgraded the clamp to fit his bars and repositioned it to fit his hand position.