I am a Small contractor. I do 15- 20,000 per year. I recently did work for a much cheaper rate to help someone out for cash. They paid me with a check made to cash.If I cash this check do I have to claim it on my taxes?

Yes. Why would you think income would not get reported? You have to endorse that check to cash it or deposit it and that shows ownership. If you want to try to under the table you could but it may not be worth the chance.

Actually, if you are only making $20,000 per year, I wouldn't expect that you would have to pay any income tax. And if you are married, filing jointly, particularly if you have minor children, including that income in your return (which you are by law required to do) might actually increase your refund.