I have a friend who had tonsillitis OFTEN as a child but her mother chose not to have them removed for the same reasons as JoanneK mentioned. Also, children are meant to grow out of tonsillitis. But my friend now is 27 and has at least 1 or 2 BAD bouts of tonsillitis every year, lasting from one to three weeks each!! It seems dumb to me that 20 years of suffering with this EVERY YEAR could have been avoided by a simple operation when she was 10.
I had my adenoids out when I was around 10 - before that, I couldn't breath through my nose at ALL, EVER... adenoids are exactly the same type of tissue as tonsils, just at the back of your nose instead of in your throat. Getting them out was an awesome decision - even when I have the WORST cold ever, my nose and breathing is MUCH better than before I had my adenoids out.
If my child ever was recommended to get their adenoids or tonsils out due to repeated infection, I would get them out IMMEDIATELY. It really is just a minor surgery, in Australia, it's even performed as day surgery. And in my experience, the benefits were IMMEDIATE and LONG TERM - as opposed to the 20+ years of continual sickness that my friend, who chose NOT to have them out, suffered.
I know those are only two cases, and there is lots to consider - but don't be scared of the surgery - it could be the best thing you choose for your child, I believe!! Of course, you want to be as informed as possible about your child's condition before you make that decision though - but don't let people talk you out of it either!!