I guess it depends on the age.
Children
There are a few ways that i deal with quiet children. If i am asking the class questions and no one is responding, I have everyone stand up. Then I get them to do a little exercise. I know it sounds silly but sometimes they just need to be revitalized. They could do jumping jacks or just walk around in a circle or whatever.
A variation to that is to walk around in a circle and when a student answers my question, they can sit down. That's when the answers start flying out of their mouths. Usually you will never have to do this more than twice, because they will get tired of walking around in circles.
Remember, these students have been sitting in class all day having fact after fact thrown at them. Their blood needs to get flowing. The exercise is silly but it helps to revitalize them.
Also for children, the
The Slam Game works really well. Then they are forced to speak.
Adults
This is a bit more difficult. If they aren't responding to you, try some group work. It might be they just don't feel comfortable with their classmates. Get them to get to know each other. Once they feel comfortable with each other then they can start to express themselves ie. speak more in class.
Try surveys where they have to gather information from other students in class. Or pair work where they have to learn things about their partner.
One thing i did with my adult classes is had them bring in topics of discussion. that way, they are bringing things that interest them.
If that fails, just be silent and wait for them to respond. Eventually they will, but you have to be strong enough to get through those painful silent moments. But DONT let them off the hook.
Last resort, guilt trip. Why are you here? Do you want to learn to speak English? Etc...
Good luck and let us know how it goes.