My Canon 550d is new and right out of the box on full auto indoor pics are dark. If I go to no flash mode they are much brighter. It's like the flash is out of sync. Is it the camera or me?

The flash only covers a certain range and the built in flash has quite a small range. so lets say its dark in the room and you take a shot of a person they probably look really bright but the background is pretty dark, thats pretty normal and its better not to use flash, now in the auto mode without flash it will be using a higher "ISO" number to get you brighter shots indoors. shots may look slightly grainer but it means its brighter and the 550d handles low light pretty well.

in auto mode you have no control over the ISO but put the camera into P mode which is basically auto but with access to more controls which you can override. now next to the shutter button there is an "ISO"button. experiment with the different numbered setting (100 being low 3200 being high) and you will see what I mean