Hey Charlene, some more nice flat resistant tires that are easy to find around here are Bontrager Race Lite Hardcase (Bicycle Sports Pacific, Cap's) and Schwalbe Marathon Plus (Bikes on the Drive, Dream). The racelites are a little sportier with no tread, and the marathons have a bit of knob to em, but i haven't flatted yet with either tire.

That said, other posters are correct that lots of flats are due to mechanicing without knowing quite what you're doing. Every cyclist has to go through that, and eventually it subsides a bit.