What is a great collaborator?

What makes a great collaborator? Is it different than being great on your own? Does one come at the expense of the other? I have a couple examples from popular music I think about frequently...

Eric Clapton is about as celebrated as anyone in modern popular music, but many of his most famous songs are covers or collaborations with other luminaries. He wrote "Layla" with the immortal Duane Allman, several of his hits were covers of songs by the excellent but more obscure J.J. Cale, and even his early group Cream was thusly called for being a super-group.

Run the Jewels provides a different sort of case study because both its members have maintained vigorous parallel solo careers. This is only my opinion, but I think the two members are much better together than alone: Killer Mike is prone to bogging down in southern rap idiom while El-P gets lost in grumpiness and misanthropy. These vices seem to vanish when they are together.

What do you think? Is there such thing as a great collaborator?