Condiment for onion rings (and fries): equal parts ketchup and mayo, and a tablespoon or so each of Worcestshire sauce, Grey Poupon, and/or horseradish.
For my burgers, I will mix into the meat: two diced cloves of garlic, two teaspoons or so of spicy mustard, salt, pepper, and some thyme. I may add a shot or two of Worcestshire sauce as well. Make sure when you make the patties that you put a little indent in the center with your thumb so they don't turn into balls on the grill. NEVER EVER EVER EVER flatten them with the spatula like you see on TV. NEVER. It forces all the juices out making a dry, tasteless burger.