Usually, when we bump into people or tread on each others toes or something like that, both people tend to say sorry. A normal exchange would be like this:
Don't say No problem or never mind or anything like that. The person is saying sorry to be polite. They probably don't feel that they have done anything wrong. They just want to be friendly and polite. Saying sorry is just a way to show that we are friendly. If you say never mind or no worries then there's a chance that you will annoy the other person. This is because you may sound as if you feel they should be sorry. They may not feel that they should be for such a trivial thing. So, just say: Sorry! And smile.
This is definitely the situation in the UK. I believe it is similar in the US.