Luc - To my knowledge you can play non-ladder, ladder, and hardcore characters but they can't go into games with the other kind of character. In other words, your ladder character can't play with your non-ladder character (as we've already seen) same thing with your hardcore character.
Just in case you don't know - a hardcore character is one that only gets to die once. If it dies you can't play it again. <img src="/ubbthreads/images/graemlins/cry.gif" alt="" />
In single player (on your own computer) you can't create a hardcore character without having made it through Hell. That doesn't seem to be true on BattleNet. I have a hardcore character and I haven't made it all the way through there yet.
Hope this helps! <img src="/ubbthreads/images/graemlins/smile.gif" alt="" />