Will slightly loose bearings result in damage? I just overhauled some cheap bmx hubs. I installed new bearings and cones. Now I'm trying to get the hubs adjusted so that the bearings will last as long as possible.

I had always thought that leaving bearings even a tiny bit loose (be it bb, pedal, or hub) was one of the cardinal sins when it came to maintaining a bike. But reading this from Sheldon Brown put that in question:


  If nothing you can do will eliminate both the binding and the play at
  the same time, it is better to adjust a little loose and accept a
  slight amount of play then to have the hub bind


This is the situation I'm in. Is a little bit of bearing play a legitimate option? Will my bearings wear down more quickly if they are slightly binding or if they are slightly loose?
A bearing that is adjusted too tight can actually seize completely. This happened to me once. I overhauled my front hub and tightened the bearing cones too much. Result: a front wheel that plain stopped turning at some point. 

Too tight adjustment will exert more pressure on the cones and cups, and will probably wear out the bearings faster than too loose an adjustment. 

For proper adjustment, the Park tool website has good instructions: http://www.parktool.com/blog/repair-help/hub-overhaul-and-adjustment