I don't worry too much about alliances, I just break them if they're going to drag me into a war I don't want to fight. Unless you're trying to win a diplomatic victory and have somebody join you peacefully, the only real use for a very good relationship with another great power is to get access to trade with their colonies (computer GPs automatically have their colonies boycott everyone, unless your relationship is in the green zone). If you've got a lot of excess industrial product, the late-game treasury of a foreign colony can be a big help. Otherwise aim for "just strong/nice enough that they don't declare war on me".

Alliances are useless. The AI is flawed, so in the end you will be fighting pretty much all of the major powers (at least on harder difficulties).