I'm not predicting which movies will be nominated, but I will predict that the total grosses for the three Best Animated Film of the Year nominees will be at least be equal to, and probably double the total grosses for the five Best Picture nominees.
Now the results are in, and I was right! (sort of, follow the link back to the original post if you want to see the details that were wrong, that one paragraph I pulled was spot on, though)
The three animated nominees were Cars $244M, Happy Feet $191M, and Monster House $74M, with an approx. cumulative total of $509M dollars (I thought Monster House was the best of the lot, bet it got lost in the shuffle and deluge of these sort of pictures this Summer/Fall).
Compare that to the five best picture nominees, Babel $24M, The Departed $122M, Letters From Iwo Jima $3M, Little Miss Sunshine $60M, and The Queen $36M for an approx. cumulative total of $242M. (I can't make a pick out of these, the only one I saw was Departed, and that's no Best Picture in my opinion).
Cars alone beat the total for the five Best Picture nominees, and if it weren't for The Departed's $100+ performance, it wouldn't even been close.
In no way shape or form should The Departed deserve to be considered one of the five best films of the year, it was an overly long exploitation/action picture with delusions of grandeur, nothing more (though it was enjoyable if you have a tolerance for violence). Had the director not been named "Marty", and the lead ham not been named "Jack", then nobody would have considered this film as anything more than what it was.
If I were doing the choosing I'd only choose two Spanish films for Best Picture, and skip rounding out a top five as both Pan's Labyrinth and Volver are that much better than anything else I saw in 2006 (and admittedly, I avoided more films than I saw this year), that to round out the list with 3 other pictures would be pointless.
This prediction could pretty much be a standing prediction for the next decade or so. The 3 animated nominees will most likely dwarf the box office of the 5 best picture nominees, unless something like a Lord of the Rings breaks through and gets critical praise, but those events will be rarer and rarer.
What could change that is the glut of 'kiddie' CGI pictures. Academy members may seek out animation aimed at an adult audience and ignore all the big spring/summer/fall popcorn pushers (if Through a Scanner Darkly had received more wide acclaim, it might have been nominated as an animated picture this year). Also, as the tools for making these films get cheaper and cheaper, it won't just be pictures designed to gross $200M and garner a wide audience that will be made using animation techniques.
Clearly, the Academy views this category as the 'kiddie' category, and it would take a concerted effort by a studio to challenge that assumption to get a more 'serious' picture considered in that category but it seems like that should happen at some point as despite their increasing irrelevance, Oscar nominations are still used as a marketing tool.