Pact of Research in Civilization V
What are the requirements to have the option to sign a Pact of Research with another Civ?
Both sides need enough money for the agreement, and at least one side has researched Philosophy.
The cost for a research agreement scales with the era of the more advanced player and with the game speed:
Era Quick Standard Epic Marathon
Classical 134 200 300 600
Medieval 167 250 375 750
Rennaisance 167 250 375 750
Industrial 201 300 450 900
Modern 234 350 525 1050
Future 234 350 525 1050
You can also have only one active research agreement per civilization, and research agreements are not possible during war (as bwarner pointed out).
If the enemy civilization has not enough money for the research agreement you can also gift (or loan it against gold per turn) the necessary gold to them.