My kind of party is one in which I don't have to bring anything!
As for me, if I am the host then I feel that I should provide food, refreshments, etc. I never "require" anyone to bring anything, however, I wouldn't feel bad if someone showed up with something. If one of my friends or family is having a party, I may bring a bottle of wine, cake, brownies, or something that I have made (I like to show off my baking and cooking skills
) that I think everyone will enjoy. It's done out of love.
I feel that it is in poor taste and etiquette to require someone to bring something to an event that they are hosting. I feel that the only time that it's cool is if I know that my girl can throw down on some deviled eggs and I ask her to make a batch for me. Then again, being the person that I am, I'd probably just ask for the recipe. In our family, someone specializes in one or more things, so they'll make their dish and bring it (pot luck), however, the family member that hosts the event usually makes the bulk of the meal and everyone just brings things to add on.
Simply put: Don't invite me to a barbecue and tell me that I have to bring the ribs. You host, you buy.