Is passenger weight distribution important on a commercial flight? This is something I've wondered about for a long time.  On really large airplanes, like a 747-400 or A380 for example, I would assume that the weight of the passengers on board is a significant to the flight characteristics of the plane. And it seems like it would be pretty easy to put all the passengers in an odd place (like all at the front or back) and as a result significantly change the flight characteristics of an aircraft.

So, assuming I'm right (tell me if I'm not), how do commercial aircraft counter this problem? Do they do their best to distribute passengers throughout the craft with seat assignments? Or do they have ballast they can move around (like fuel ballast)?  Or is the weight shift not significant enough to warrant anything along these lines?
On the EMB-145 the passenger cabin was split into 5 zones and we were given passenger totals in each zone from the flight attendant prior to leaving the gate.  If balance is off (this happened quite rarely for us) you would tell the flight attendant "I need 2 passengers from zone 5 moved to zone 1" or "I need a passenger from zone 3 moved to zone 2" or some other similar instruction.  The flight attendant would solicit volunteers and if no one did, they would instruct someone to move.  The move was only for takeoff and once airborne they could go back to their normal seat.

After moving passengers we would re-calculate the weight and balance to verify we were in the envelope and set takeoff trim.

Similar methods are used in larger airplanes with the cabin split into zones.

The only time we would use ballast is when we had a full cabin and not enough bags in the cargo (not common).  In those cases we would ask ops for ballast and they would put something in the cargo.  They would try to make it useful if an outstation needed something else they would just load 50 lb bags of sand.