The best time to use a coupon is when there is a sale. You will get more "bang for your buck" and save more money.
The next best time, is if you need the item (example: toilet paper) and it's a critical low time in the house, you can't wait for the next sale cycle in the store... make your own "sale" by using the coupon. At least you are still saving "something" and not paying full price.
The best time to try a "new" product on the shelves is when you have a coupon! When a new product comes out, product taste testing in stores or demonstrations for a products effectiveness are usually performed. This is also when they hand out coupons (sometimes) and this is when you will find the product on special (sometimes). Use the coupon (watch for Smart Source, Red Plum, etc for "new" products about to hit the shelves, and have your coupon ready for when it arrives in stores).
This is when to buy a product, on sale with your coupon, when it's new. Then, if you don't like it; it's not as big a ding to your pocket-book!