Two important things which I have learnt from Hunter x Hunter:
1. Always be true to yourself and work hard accordingly.
I can see this in quite a number of cases, like when Gon and Killua were training against that guy during Greed Island with Biske supervising them...they could have easily finished their training but they chose the hard way to improve themselves and being true to themselves.
2.If you want to get stronger (not necessarily physically) always go into the basics and understand it thoroughly.
There are numerous times where Gon and Killua train like in the Celestial Tower, in Greed Island and even during their training before their fight with Knuckle and Shoot, Biske always tells them to focus on Ten and developing their Nen...
Hm i guess true passion... It sure was for me a great thing when i was a kid and just started to read the manga=) Gon was chasin his dad with passion. Hm let me think wat else it taught me... Freedom. Gon has true freedom. He could do wateva he wanted to do which makes me feel of true freedom... and also curiosity=) Gon showed me wat real curiosity means=))