Caveats: This was only done with a single character, a level 60 Wizard. This was ONLY done in Inferno A1, due to ease of killing. I would not be surprised if different acts or different classes saw vastly different results. The first run was a complete clear from the very beginning of A1, the rest started at Reign of the Black King and went through the end of the act. After my last full run, I needed just a couple more elites to reach 100 for a good data sample, so I reloaded, went to The Festering Woods, and ended up with 1 champion and 3 elites, bringing my totals up to 150 champions and 101 elites.
Also, some packs were not recorded. In four cases, the Dark Moon Shaman bug was in play, and while I could figure out 2-3 affixes for each pack, I couldn't figure them all out before they died. Those results were tossed out. There were a couple cases where I thought I'd gotten good screenshots, but ended up missing them due to trying to take pictures while running in combat. Finally, there were about three or four packs that simply melted to Archon before I could get a screenshot off. Oops.
Individual Affix Results: http://i.imgur.com/sBnMF.jpg
Most Common Affix Pairs: http://i.imgur.com/eZgek.jpg
Champion packs liked to have Reflect Damage (38), Teleport (37), and Plague (35), while Avenger (15), Extra Health (16), and Shielding and Nightmarish (19 each) were relatively rare. For Elites, Arcane topped the list (34), while Frozen and Waller (29 each) weren't far behind. To my utter lack of shock, Missile Dampening was by far the rarest affix of all (4), but Elites didn't like Vampiric (6) or Illusionist (8) much either. Overall across all packs, Arcane (61) had the best chance of showing up, followed by Frozen and Reflect Damage (58 each). The first pic linked has the full list, including the percentage each affix showed up (Reflect Damage showed up on over 25% of all Champion packs, for instance!)
I also wanted to see which affixes liked to show up with each other, so I did a little more digging. The full list of affix pairs was just too long to post anywhere, but the most frequent ones are in the second pic linked above. For Champions, Desecrator & Reflect Damage (11) paired together the most, followed by Electrified & Molten and Knockback & Plagued (10 each). Elites liked to pair Vortex & Waller for some reason (10), with Arcane & Fast, Arcane & Frozen, and Frozen & Mortar (9 each) also relatively popular combinations. Across all packs, Arcane & Fast and Vortex & Waller (16 each) had the best chance of showing up together, followed by Desecrator & Reflect Damage (15).
Overall, I enjoyed the quest to finding all of this out. In the process, I discovered that at least for me, Champion Packs outnumbered Elites 3 to 2, and I did indeed confirm that Missile Dampening just does not like showing up for me. That is kind of disappointing; it's an extremely fun affix to play against as a ranged class.
For anyone who wants to see the entire list, or doesn't believe the numbers I came up with and wants to check my work, I have the raw data up at https://docs.google.com/spreadsheet/ccc?key=0ApYVpYaeH7nMdF9CRUhYXzBseG9XLTBmMkxDd2xwYWc. Now, back to farming!
Edit: Tribun caught an error in the single affix Combined Results. That's what I get for not triple-checking at 1:30am. Thanks!