Resign if you feel like there is nothing left for you to learn in the game, if you don't feel like continuing, or there is no hope of getting a draw.
Some people complain if you don't resign in such positions and some do if you do. The only person you can please for sure is yourself. 
Your question relates to an eternal debate that is happening every day on this site, in some corner of the forums.
http://www.chess.com/forum/search?keyword=resign
Generally speaking, most people here would agree with Martin's advice.
It can be considered rude to play on in a hopeless position (down 8 points or more), especially with slower time controls. In blitz chess however, it's pretty common for people with a lost position to try to win on time or with a lucky combination or fork, so always go for the win if your opponent is in time trouble or if you have a knight on the board.
I'm new. I don't wish to waste anyone's time. Thanks!