Loose connection somewhere on the circuit. If it is more than one circuit then a loose connection in the panel. If your panel is fed from a fused disconnect in the main electrical room then it be there as well.

Not enough information. For the bathrooms I suspect you have caused a ground fault. Did you try to reset the GFCI?

"I'm not very knowledgeable about this, but I am to understand you can use a regular GFCIO in a two wire house system and it will work as a GIF? Why do you need a ground if you are using the GFCI." A GFCI does not require a ground to operate correctly. It senses if the current between the hot and neutral do not match within 0.005 amps, and then shuts own the circuit. It provides personnel protection, that in many ways is superior to having a 3-wire circuit. A groundING conductor (AKA 'safety ground') provides a low impedance path to allow an over current device (fuse or breaker) to trip. It provides protection to the equipment that is plugged into the 3-wire circuit more than anything. If the hot wire comes in contact with a metal chassis, enough current should flow to trip the breaker. If you are between the hot and ground it is extremely unlikely the current will ever approach the level needed to trip a breaker. You will be in the circuit until you remove yourself, possibly by becoming unconscious and falling. While it is rare for 120 V to push enough current through the heart to cause problems, under the wrong conditions it can happen ... wet or sweaty hands, solid contact, 120 V appliance in the tub with you (the drowning is actually often the actual cause of death, becoming unconscious in water is never a good idea).

"Only the breaker would, if enough total current was passing." Well, sort of. Just to dispel any possible confusion: A GFI breaker implements two functions. The first is overcurrent protection. The breaker trips if the total current drawn from the circuit exceeds the breaker's rating. For branch circuits this is normally 15 or 20 amps. The more it exceeds the breaker's rating, the faster the breaker trips. The second is ground fault protection. The breaker trips if it detects that the current is asymmetrical across the power line. The amount of asymmetrical (ground fault) current that trips the GFI part of the breaker is MUCH lower than the current that trips the overcurrent part . (Confused yet?) To explain this second function: it's not 100% accurate to describe it this way, but it's easier (I hope) to understand if you think of the electricity as going out the hot side of the receptacle and coming back in the neutral side. The GFI monitors both of these. If the amount of current coming back is less than the amount going out, some of it must be "leaking" to ground. That leakage might be going through a person or animal, risking shock or electrocution. So when the GFI sees that, it instantly opens, shutting off the power. With most GFIs, an imbalance (fault current) of 5 milliamps (0.005 amps) is enough to cause a trip.