I have to partially disagree with PaulRivers' conclusion.

Higher air pressure results in lower rolling resistance, all else being equal. Also, wider tires have lower rolling resistance than narrower tires, all else being equal. But all else is rarely equal, unless you are discussing tires of the same model, and similar, but slightly different sizes.

Consider two tires, same model, one 32 mm, the other 35 mm. There is a lot of overlap in their respective ranges of tire pressures, so they can be run at the same pressure, in which case, the 35 mm tire will have lower rolling resistance. Or, thought of differently, the 35 mm tire can be inflated to a lower, more comfortable pressure, while retaining the same rolling resistance as the 32 mm tire. As long as there is some overlap in the range of allowable tire pressures, we can make a wider tire have lower rolling resistance at the same pressure or the same resistance at a lower pressure.

However, most narrow tires can be inflated to higher pressures than wider tires when the difference in width is very much. In many cases, this allows the narrower tire to achieve a lower rolling resistance than the wider tire. Sort of.

This all assumes a perfectly smooth surface for the tires to roll on. In the real world, perfectly smooth pavement is pretty rare. When an irregularity is encountered, whether it be a small piece of debris or a bump in the pavement, either the tire has to give, conforming to the surface, or the bike is lifted over the irregularity, which requires more energy. When the bike has to be lifted, the energy to do so comes from the bikes kinetic energy. Most of that energy is lost. So it is desirable to run a tire pressure that is low enough to allow the tire to absorb the impact of such irregularities so the bike doesn't have to be lifted at ever surface irregularity.

This same principle is what makes full suspension mountain bikes faster over very rough terrain than their rigid counterparts, all else equal. The suspension absorbs the bumps, requiring the rider to be lifted less, conserving more kinetic energy. On smooth pavement, however, the lack of suspension helps stabilize the rider vertically, compared to the full suspension bike, making the rigid bike faster. (Here, we assume typical mountain bike tire pressures, low enough for tires to absorb the overwhelming majority of road surface irregularities.)

Most pavement isn't perfectly smooth, even when new. This means that, in the real world, for non-racers who aren't terribly concerned about the additional small amount of air resistance, it is better to decrease rolling resistance via increased tire width instead of increased tire pressure. The rougher the roads anticipated, the wider the tire needed to minimize rolling resistance.

All that being said, rolling resistance is overrated, and wider tires allow for a much more comfortable ride. A more comfortable ride will contribute much more to most people's cycling enjoyment than will decreased rolling resistance. And, as has been pointed out, wider tires will allow better cornering!