Well, as a nurse since 1990 - I can honestly say, I've never ever seen anyone die as a direct result of general anaesthesia. When working in theatres as a student, I once saw someone die in theatres, as a result of a dissecting aortic aneurism - nowt to do with the anaesthetic however... I do know that the plural of anecdote is not data
I've had several GA's meself, and been fine.
Ds1 when 11, needed one for plastic surgery on his finger, after someone trod on it - it dislocated, and broke across the growth plate, and his nailbed needed plastic surgery, so he could grow new nails, and also to put said finger back into place, so his finger could grow etc...
I went into the anaesthetic room with him - they put on the monitoring pads, sats monitoring, BP cuff, cannula in, we were laughing and joking together - then they put the fentanyl, anti-emetic, and propofol in, to induce him - and as soon as he drifted off - I howled!
The nurse that was with me was very good, and recognised that however comfortable I was with the idea of a GA - seeing your child drift off with his first GA- is a different emotional scenario 
He was absolutely fine :O