Believe it or not, it is actually possible to run the Boston Marathon without qualifying. In order to do so, you need to apply through one of the official Boston Marathon Charities.
You can find the full list of supported charities here: BAA Official Charities
Just keep in mind that you need to make contact with the charity of your choice to initiate the application. You also need to raise at $5,000 for the selected charity.
So either you need to run a super fast qualifying time, or you need to raise $5000 for one of the official charities. Those are basically the two ways to gain entry to the Boston Marathon.