I know there are many sites which will allow me to find a flight to wherever from a given airport, but I haven't found one that would allow me to specify a destination and no starting location. Are there any? (Obviously, I'm looking for cheaper flights)
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If you could yourself limit to an airport and all airports within a 2000 miles radius, then Google's Matrix Airfare Search could be an option for you. Generally, all matrix flight search engines could be interesting. I did your specific search query for you and checked all the flights from Berlin, including all other airports within 2000 miles radius, to Bergen for January 2013:

If you select one of these dates, you can see the specific flights. For example for the cheap flight at January, 13., you get a list like this:

Kris
- 9,840
- 3
- 54
- 68
RoflcoptrException
- 51,590
- 52
- 190
- 403