Here's a handy tip I just learned from celeb chef Gail Simmons: Marinate your onions in salad dressing before you add them to your salad. It's easy. When you go to make your salad, start by chopping or slicing your onions and then pour a vinegar or citrus-based dressing over them. Let them soak for about 10 or 15 minutes and their heat and flavor will mellow considerably. Then toss them and the dressing into your salad.
You can always strain the onions before adding them to your salad, if you've used more dressing than you actually want to eat.
By the way, the big exception to this are green onions -- thinly sliced green onions are great raw in salads.