Can I use a GSM phone on all GSM networks or a CDMA phone on all CDMA networks?

We will start with GSM phones. You can use a GSM phone on another GSM network if it has been unlocked and if the carrier and phone operate on the same frequencies. When a GSM phone is put out by a carrier (AT&T or T-Mobile for instance), the phone is "locked" to that carriers network. To remove the carrier lock, known as unlocking, you can either request the unlock code from the carrier or purchase the unlock code from a secondary company (check ebay or google "unlock code"). Regarding the phones operating frequencies, generally most cell phones produced are quad band; they operate on all 4 possible GSM frequencies. Quad band phones can be used on any GSM network worldwide. If you want to know what frequencies your cell phone operates on, we recommend checking phonescoop.com. You can look up the technical details of any phone on that site. You can contact your carrier and see which frequencies they operate on in your particular area.
With CDMA phones, you can not unlock them to be used on another CDMA network. You can "flash" them to another CDMA network. This requires having the phone reprogrammed for the other carriers CDMA network, and not all CDMA networks will accept a phone that was on a competitor. Verizon and Sprint will not activate a phone that had previously been on another network once it had been flashed. Cricket and Metro PCS will, but charge an additional fee for the activation.