Any sites that allow you to name your own price, e.g. priceline
Employee tickets and some consolidator fares also don't earn miles, but you have to ask the consolidator to find out.

Programs that has status last more than 1 year and have more than 1 year to accure for status, OZ.
However, OZ is only good to get the status, but not good to earn or use their miles, as the redemption rate is poor (require significant more miles to redeem awards), elite bonus is not much.