The Eagles/Giants rivalry is incredibly intense- in some cases I think even more intense than the rivalries against the Skins or the Cowboys. My friend has season tickets to the Giants and he says that it's consistently the game each year where the most fights break out in the stands. I was actually at the Eagles/Giants game this year at Giants stadium (where McNabb got sacked 12 times), and literally every 10 minutes somebody was getting thrown out of the game for fighting. Conversely, I was at the Giants vs. Jets game the very next weekend (which isn't really a rivalry at all- but they do share a stadium) and there wasn't even one fight.
Philly vs. NY/NJ sports teams extends well outside of football- Mets vs. Phillies, Flyers vs. Devils/Rangers (Scott Stevens blowing up Eric Lindros
), Knicks vs. Sixers. The two cities are only 90 miles apart, and both essentially share NJ as a suburb.