Michael Scott vs. Toby Flenderson (The Office)
This is about as much of a true rivalry as the Harlem Globetrotters-Washington Generals series. Like the Globetrotters, Michael always wins. From mean-spirited divorce jokes to cracks about Toby killing the fun in the office, Michael just constantly abuses the head of human resources.
As with the Homer Simpson-Ned Flanders dynamic, no matter how hard Toby tries to be nice, Michael can't tolerate him.
There was also this, which I imitate every time the summer ends and a new school-year begins:
So, yeah, this rivalry should have made my list.