Get a regular playing card or index card for each child in your class. Write each child's name on a card. Shuffle them up and get ready to ban hand-raising in your classroom. From now on, whenever you ask a question and need an answer from a student, you will simply pull a card from your deck, rather than calling on hand-raisers.
There are many benefits to this simple technique. First of all, it eliminates favoritism from the teacher. No longer will you call on those few students who seem to always have their hands up. Nor will you be able to continue ignore those silent and/or shy kids that seem to shrink away when you ask for a response. Additionally, each and every child will have to pay closer attention to your words and the responses of classmates. The children never know when they will be called on and they aren't allowed to repeat what someone else already said.
Oh, and don't place just-pulled cards onto the bottom of the deck. Slip them into the middle, maybe even near the top, so that the child who just responded can't sit back and rest assured that he won't be called on again for quite awhile. At first, you may even want to make sure to call on the same child two times in a row, just to demonstrate that you're never "safe" from answering a question.
When I first announced this change to my class a couple weeks ago, the students were a little thrown off. Now, if I even look like I might call on a hand-raiser, they remind me to use the cards. I have noticed a difference in the amount of participation I receive and it's from a more diverse population as well.
Of course, there may be exceptions to the card rule where hand-raising works best. But, give this simple technique a try and you might be surprised at the magical changes happening right before your very eyes.