I've found alliances useful in the early game if I want to concentrate on expansion. On the world map, as the Americans, I either wipe out the Aztecs or ally with them. If they're my allies they may take one or two city spots I wanted, but basically I don't have to defend against anything other than Barbs at first, and I grow fast.
I've also had some very long-term alliances. One game on the European map as England I allied with Spain very early, helped protect them. We colonized North Africa and the Mediterranean together even though the AI almost always ignores North Africa. It was weird, our cities were intertwined (England-Spain-England-England-Spain...). If our alliance had ever broken up we'd have both been screwed, but it lasted until my spaceship victory. The fact that our territories overlapped so much meant that we both sent units after Barbs.