So far the answers have been about Road tyres But I am an offroader. I use Panaracer Fire XC's on all my MTB's as it suits my terrain. On the Solo I use 1.8's and run them at 50PSi for my meagre 150lbs. This will stop pinch flats and they roll pretty well but still give grip. I occasionally use the 2.1's and use the same pressure.
Now on the Tandem- a lot of teams use 2.3 tyres or larger. I still use the Fire XC 2.1's and run them at 60psi- which puts them at the top of the pressure rating for this tyre. Still gives grip and due to the construction of the Fire XC, we do not get pinch flats. That is for our 400lbs all up weight on the Tandem. I did at one point use IRC Mythos but got pinch flats at 60psi, although the grip was good. Had to go to 75PSI to stop them on this tyre, and at that pressure, we were losing grip.

Like a several of the Road tandem teams- I have found that you do not have to go wide- just because it is a tandem. Tyre pressure is all important, and that is dependant on the tyre construction and the weight of the team. Whatever pressure you do use though- Do inspect the tyre frequently for sidewall damage, and every now and then, Say every 6 months- take the tyre off and inspect the interior of the tyre and the tube. Suprising how many marks we have on the tubes from in and out thorns and flints, and how many times we have found the cords of the tyre lifting away from the rubber, just where the flint damage is.