4, 5, 6, and 7 I've seen; never seen a 9 pin. If you'll go to google.com and enter "trailer light plugs" and "trailer light connectors" you'll find more than you want to read on the topic. The 7 pin connectors that I'm familiar with are: (1) ground, (2) taillights, (3) left flasher or turn signal, (4) right flasher or turn signal - the flashers are also the brake lights usually, (5) electric brakes, (6) 12v continuous - to charge a battery or operate a 12v refrigerator or lights in the trailer, and (7) auxilliary - sometimes backup lights on the trailer.

If it were me, I'd want the 7 pin connector on the truck, and then there are plenty of adapters on the market to go down to whatever circuits are needed for each trailer, or of course, you could put 7 pin connectors on all your trailers but only have the circuits needed wired into the trailer plugs.