(to expand on that after all - positive reputation in itself doesn't really mean much. More green blips on your radar. The only real benefit is that you can get away with more bad stuff before becoming hostile to them, which actually has some real effects)
Becoming Friendly or Allied with a Superpower doesn't grant you an awful lot of privileges. You used to become automatically Allied with every single Federation-aligned minor faction you encountered, but they nixed that back around version 2.1 or so. These days, I think the sum total of your benefits is:
You get to become Allied with minor factions that are affiliated with that Superpower much easier. eg. if it takes 10 million credits worth of exploration data/trade/missions etc to become Allied with a non-aligned minor faction, it will only take you 5 million credits worth of exploration data/trade/missions etc to become Allied with a Federation-aligned minor faction, while you are Allied tot he Federation. In other words, the same amount of work will now make a Fed-aligned faction twice as happy with you.
Naval advancement missions only spawn when you are Friendly or higher with the Federation.
As Arry implied, if you don't keep doing missions etc to build it up, Superpower reputation suffers from decay - at about 2% per day - until it falls to 75%, where it won't fall any further. Not unless you declare war on the Federation, anyway.