Since we can no longer take kids out of school, we go the end of August. While it's not as nice as mid-January, the crowds really weren't too bad, and you had the added bonus of late park hours. The only park we really had an issue with was AK. There is very little shade or air conditioning there, and it wiped us out. So, next time we plan to do two mornings at AK, rather than try to do it all in one day.
I heard from a friend that the third week in August is fairly crowded--we were there the last week. Next year, we plan to go for 12 days, so will hit both weeks.