The optimum pressure for tires gets rather controversial. Certainly the pressure rating molded right on the tire is a good first guess. I like Schwalbe's guidelines:
http://www.schwalbetires.com/tech_in...ation_pressure
The right pressure seems to depend most on the width of the tire (wider tires need less pressure), then on the weight the tire is carrying (more weight requires more pressure), then maybe the road (soft or rough wants lower pressure, smooth pavement can take higher pressure). Maybe rims a bit too: narrow rims take less pressure for the same tire.
If the pressure gets too low then it means more work pedaling, it can stress the tire sidewalls and wear the tire out more quickly, and when you hit a big bump you can bottom out, hitting the rim, which can cause a flat tire (a pinch flat) or also put a dent in your rim.
I ride 2 inch / 50 mm wide tires and probably pump them up maybe every couple weeks or so. Maybe I pump the rear tire up to 48 psi and in a few weeks it will go down to 42 psi or so. If I am hauling a big load of groceries then I do try to be sure to have them pumped up beforehand but otherwise they could go down a bit more with no problem.
But those are heavy tires and also pretty thick tubes. If you have skinny lightweight tires like racing tires, those you really do want to pump up before every ride. They lose air more quickly, have less air in them anyway, and need to stay at much higher pressure to avoid pinch flats etc.