It usually has to do with close proximity but not always. But the main key without a doubt has to be they play every year. As for the trophy I think it has to do with why a rivalry starts sometimes.
I know as a True Trojan our two big rivals are ucla and notre dame.
ucla because the two schools are so so close together one is public one is private the Victory bell started because of a prank theft look here http://usctrojans.cstv.com/trads/usc-bel...

The Notre dame rivalry had somethign to do with wives wanting a travel but it's an awesome thig to be a part of. read here: http://en.wikipedia.org/wiki/Notre_Dame_...

well if they are in the same state, or if the states are right next to each other, or if they are both at the same level every single year and it just turns into a rivalry

There are a few things that are need to have a good rivilry. First both teams are generaly top tier teams (michigan vs ohio state football) They must play each other every year to keep it going. They have die hard fans who will be devisted if there team loses. IN most cases but not all they are in the same state or interstate.

the michigan Vs oho state is one reason i belvie J Cooper was fired a few years ago from ohio state.. he just could not beat michigan

usually they are close to each other - along with that, most of the students decided to go to one school over the other, so they think their school is better. They also play each other every year