Switching cell phone carriers while keeping same iPhone?

Can I keep my iPhone and switch carriers w/out getting a different phone & also (if possible) w/out jail-breaking my current one. I ask this because the box on my iPhone doesn't mention any particular provider.

Also answer this please: http://answers.yahoo.com/question/index;_ylt=AuAnjVUKF0bS3AiWejfehSYM_dw4;_ylv=3?qid=20121130203559AAMcoEp

Yes you can just go 2 the place and do it there

Yes my son did that