The rules say that cards in play must be traded or discarded. When can I discard them?

This depends on the type of card. First, it must be in play in front of you (no discarding other people's cards, silly). Race and Class cards (including Half-Breed and Super Munchkin), and other similar cards, can be discarded at any time, including to power a special ability, but not an ability for the discarded Race or Class (unless the ability requires discarding that particular Race or Class). Curses that remain on the table in front of you cannot be discarded. Item cards are the only cards that can be traded, and, as long as they aren't prevented from being discarded (say, by a Curse), can only be discarded in the following ways: As part of a sale To power a special ability of a Class/Race or another card To fulfill the requirements of Bad Stuff or a Curse/Trap/Disaster The Item is Big and you MUST get rid of it (e.g., because your Hireling died or you are no longer a Dwarf), and there is no one who can take it