There are generally 3 reasons why people want these:

1) A consistly lousy monitor mix by either the sound engineer or the guy doing it from the stage or the lack of usable feedback from the band to the mixer to get a better mix. If you think the monitors are loud enough, but you still can't %$#^&!, this may be your problem.
2) It's too loud on stage and the band is sick of it. Someone suggests in-ear monitors to reduce the volume. This is frequently caused by problem number one.
3) The desire to make it LOUDER on stage.

#1 and #2 are not bad reasons -- both have better solutions but not necessarily easier ones, and can help save your ears.

#3 is dangerous unless one has a hearing problem. Like all headphones, people tend to turn them up louder and louder until significant damage can be done. (Including to people who already have hearing problems.)

For those with hearing problems in ear monitors can be a big help. But, before sticking ANY speaker in your ear and turning it up, get a through hearing test to help determine your specific issues. If you can target your weak areas with a better mix and/or EQ, you can prevent further damage. For example, I can't hear much at all from 2-6k in my left ear, and am totally deaf at 4k in that ear. If I were to get one, I'd stick an in-ear monitor in the left ear and boost just the frequencies I can't hear. The net result could help me hear without damaging what's left of my hearing.

As for choosing which ear, most people have a dominant ear. You know which one it is, even if you haven't thought about it before. It's probably the ear you use the phone with, but it might be the one you use to hear harmonies.