Well, I'm 31 which still felt pretty young until I read this thread
I got into TNG once they've finished making it while researching a university project (about Cult TV). One of the first episodes I watched was "Attached" and I became a P/Cer that day and still am. I then went back to the start of the series and watched all the eps in the space of a few months and started going to conventions. Favourite character: Picard. As well as being sex on legs he's also the sort of person you aspire to be like. I certainly think getting into TNG made me a more tolerant person. Closely followed by Crusher. Whilst I have enjoyed all the Treks to some extent TNG for me has that chemistry and feeling of family which has yet to be replicated.
I enjoyed the movies but don't consider them TNG in the same way as the series. For me AGT was the finale to Next Gen and about as good as you could wish for.
Living in the UK I've had the opportunity to see Patrick Stewart on stage 5 times over the last few years and am looking forward to seeing him do Shakespeare next year - something I've wanted to see since I first got into TNG.