Do you enjoy a combined family and radio holiday ? Or are you working abroad and 'radio activity' is an option? Or perhaps you are totally nuts (according to your XYL) and prefer spending your money on a DXpedition?
Odds are you will make transmissions from a 'wanted' entity. The more wanted, the more chances you'll have to encounter situations as above mentioned: 'cops', nobody listening to your instructions, etc. It is very important that YOU control the situation, and keep it under control.

How can you control a pileup and keep control? Indeed, while not a simple assignment, it is totally feasible. Here are some tips:

If a pileup grows too big on you, you may decide to work by continent/region or by numbers.
Working by continent/region means you call only one specific continent (e.g. Europe) or region (Northern Europe, West Coast USA), while the DXers in the other continents/regions have to standby.
Working by numbers means you call the stations by the number in their callsign (0-9).

This way of operating is generally not recommended. Large groups of operators are sitting idle, nervously waiting until it is their turn to call you. While waiting, they have no guarantee you will call their continent or number; you can go QRT at any time. Hence they are nervous. And nervous people can quickly turn into nasty 'cops'. If you work by numbers, 90% of the pileup is sitting idle!

However, to cope with a big pileup, this way of operating may assist operators who are in the learning curve.
The one real advantage of working by continent/region is to give areas of the world that normally have poor propagation towards you, the chance to get through.

Some things to keep in mind when working by continent/region:

Some things to keep in mind when working by number:

Besides working by continent/region or number, some operators try working by countries. This is to be avoided at all times. Repeat, do not do this, you will attract 'cops' of all the 'idle sitting' nations. You will certainly fail to call each of the 335 different DX entities, so why even think about using this silly technique?

Already in 1994 Wayne Mills N7NG published a very well written book DXpeditioning Basics. It came only to my attention in June 2010. A must read for the DXpeditioner and DX station, you can find it here and here. Wish I had read it sooner!

Final remark: one of the most important points when running a pileup is to maintain the same RHYTHM throughout the operation. If you master this you will be much more relaxed, as well as the pileup. The most important point though: enjoy yourself!