If you're not really angry, "It's okay" or "Not a big deal" or "No need to apologize"

You can say "that's all right" or "that's quite all right", or "it's okay". If they are saying sorry for something more serious, you can say "apology accepted", or "I accept your apology" - which is more formal. You would not normally say one of those when somebody lightly bumps against you in a store by accident, for example.

This falls out of our mouths so frequently that it's more of a reaction than an apology. A short response is "That's OK". If we wanted to give a proper apology, we'd make a longer sentence: "(I'm) sorry for..."

Of course as everyone else said it depends on the context, but another thing you could say is "no problem"

Just one more thing to add to the long list of suggestions: There are situations where you respond to 'Sorry' with another 'Sorry'. In super-apologetic places like Britain and Canada, if you bump into another person, both of you say 'Sorry'.