Actually, I would say that the first two have almost identical meaning.
I should have known this would happen.
I should have known this was going to happen.
However the third sentence has a distinct meaning which has to do with the phrase 'to go on,' which means 'was going to continue.
I should have known this was going to go on.
In your first two sentence we know that something has already happened and is complete in the past. The last sentence means that something has continued to happen for some time. We don't really know if has stopped or if it is continuing in the present.