Hello:
I have a Hampton ceiling fan that stopped working. It is not operated with a remote. Does the unit's on & off switch go out, and is it replaceable?

Yes and yes but we need to confirm power is reaching the switch. Also check your pull chains if so equipped to be sure someone has not pulled them. Do you have a wall switch, first place to check for power. A wall switch does not necessarily have both ahot and neutral so let me know if you need help confirming power.

Yes I have a wall switch and the pull chains are intact. How do I check for power. I don't have any tools for that?

Yes you need a voltage tester or at least a test light. Do you have either or can you buy/borrow? Here is one for under $15 but you can do even cheaper at a local hardware store like ACE. Tool Profile: Voltage Tester

FIRST: Does the fan have a light and does the light work? How is the fan controlled?

Also, see here:

General ceiling fan troubleshooting and help FAQ- Ceiling Fans N More