I've always wondered why the Akatsuki's were paired.. Why didn't they choose their own partner? The more I thought about it the more it made since to me. I think they we're paired judging by their personality, interest...? let's find out. ( these are my opinions)
Deidara and Sasori were paired because they both have a thing for art. Although each one has their own view of what true art is.
1) Sasori believes "art is eternal beauty"
2) Deidara believes "art is an explosion"
Kakuzu who had more than one heart and was closest to being immortal was paired with Hidan who was immortal as you know. (they actually talk about this in the anime xD)
Itachi and Kisame were both loyal. Itachi with his village.. Kisame with the Akatsuki. (respect)
Konan and Nagato/Pein... well they were together before the Akatsuki was created. I guess they had the same dream.
The same with Zetsu and Tobi/Obito and I guess for them.. they were each following orders to create a new world.. xD (idk)