I have a credit card that has a $25,000 limit. I currently have a $0 balance on the account. They sent me a notice that said I could use a credit check and not pay any interest for 9 months. I had to pay a fee of 3% (but with a $50 maximum.)

I currently bank at Presidential Bank (www.presidential.com), which pays 3.75% on savings and 3.50% on Interest Checking. I figure I can make about $350 on the deal by putting the check in my account and collecting the interest on the balance, while paying the minimum payment until the end of the 9 months, but then pay off the entire balance a few weeks before the 0% interest rate ends.

Anyone have feedback?

Do it. Just make sure that you pay at least twice the minimum every month for those 9 months. If I were you, I'd schedule through automatic bill pay 2% of the initial amount every week (minimum payments went up to 4% per month recently)

Edited to add: also schedule a balloon payment of the entire balance at the end of promotional period. This way you will also know when your promotional offer is ending when you see a huge payment coming up on the bill pay schedule .... it is easy to forget otherwise

If you do this be careful, CC's have a habit of changing the rules midstream for basically no reason (it's in the mice print).
Better yet do you have any other consumer debt that you could transfer to the 0% CC?

I called the credit card company and they told me they would only increase the interest rate if I paid late. (I will not), or if my credit score dropped significantly. Regardless if this happens, I would be given 30 days notice. So I would just pay off the account immediately and strike it up to experience.

I have no outstanding debt outside of my home mortgage.

Absolutely do it and do not pay more than the minimum. I currently have about 25k out as well at Emigrant Direct and pay only the minimum each month (to maximize the amount of interest earned). Yes your score will take a hit but only until you pay in full at the end of the 0% term.

It's been done many times, by many people, including me. Go for it!