Always refer to your tires for correct inflation pressure. In general, you will find three pressure ranges, depending on the type of bike - mountain bikes, comfort bikes, and kids bikes will often be in the 40-65 psi range; hybrid bikes will usually be 70-90 psi; road bikes will be 90-130+ psi. Except in performance situations (i.e. rigorous mountain biking), you always want to run your tires at or near the maximum recommended tire pressure. If your tire gives you a range, inflate to the highest number. If it gives you a single pressure rating, use that.
"How often should I check my tire pressure?"
This is based off a couple different factors. Rubber is porous, like skin - much like sweat leaks out of you, air leaks out of bike tires. Over time, the pressure inside will diminish; depending on your tire size, and what pressure it contains, the air will escape in a matter of weeks, or even days. A skinny tire with a pressure over 100 psi will lose 6-10 psi in just a couple days time! Here is a general rule of thumb for good tire maintenance:
Mountain bikes, Kids bikes, Beach Cruisers, Comfort bikes (20x1.75-2.35, 26x1.75-2.7, etc.) - pressures of 35-65 psi - every 2 weeks (min.)
Hybrid bikes (26x1.0-1.50, 700x32-45+) - pressures of 70-90 psi - once a week (minimum)
Road bikes (650x23, 700x23-28) - pressures of 90-130+ psi - every 2-3 days, or every ride (minimum)