Somebody asked me my opinion on this the other day. With the amount of information we have available through the net with regards to music theory and youtube tutorials are music teachers really necessary? Even going back to the dark ages before the silicon chip, if you read biographies about famous musicians you will find that many of the greats have been self taught. How did they do it? Well, usually from listening to records and trying to work out what was being played, from watching stage performers and through experimentation with their peers.
My belief is that if somebody has the innate ability to play an instrument and sufficient motivation and time to allocate to the activity, the are going to "get it" regardless of whether they have formal tuition or not. The right teacher would probably help them get to where they want quicker though and prevent bad playing habits from happening that inhibit growth. They can also be good in keeping motivation up and broadening the students horizons.
Me? I had a term or two of piano lessons as a young child and five years of (group) clarinet lessons in high school. That was pretty much it until I studied keyboard as a mature age student at univesity. All the rest I do is pretty much self taught.
I'm going to do a follow up post for those interested about finding the right teacher. Until then, adios.