How can I create a map of all paths of flights incoming to an airport in a given day? Is there any where I could find a map overlaid with the paths of all flights that came into a given airport on a given day? 

I've found a lot of maps that show the current location of all flights, or the path of a single flight, but I haven't been able to find any that have the paths of many flights at once. 

I don't really want to scan through every flight manually, but if I could see all of their paths I could pick out the ones that have interesting tangents for further study.



Background: I recently moved in to an apartment near an airport. I enjoy watching the flights come in, but one of my new roommates is less thrilled. He remarks that some of the flights seem to be pointed directly at our building until their final turn, so if the pilots were somehow incapacitated, we'd be in trouble. I think that's geometrically incorrect, but would like to prove it.
Well you didn't state which airport you are interested in but obviously you only want data for a single airport.

You might want to look into a noise abatement reporting system. For instance, London Heathrow maintains the great website Webtrak (https://webtrak52.bksv.com/lhr4) to communicate with the pubic about changing SIDs, STARs and noise levels. (They already have much of the TMA over the heavily populated area, and they want to add another runway)