I recently wrote a post about how generic drugs work just as well as name brand medications. The same goes for many foods and household products. Unlike over the counter and prescription drugs, the ingredients are not going to be exactly the same, but most products are similar enough to be worth the cost savings.
If you have ever baked anything, you have probably walked up through the baking section at your local grocery store. I can attest that name brand sugar and flour are identical to Kroger brand as far as I can tell. For ingredients, you are probably safe with the cheaper store brand.
For prepared foods, there might be a difference. If you are a big fan of Kraft Mac and Cheese, store brand probably will not live up. However, if you care more about the food than the style, store brands will save you money.
For home goods, such as trash bags, dish detergent, cleaning products and chemicals, and so on, I only buy store brand. The products are much cheaper and are just as good as the expensive counterpart.
I almost always make an effort to buy the store brand when I go to the grocery store. I only have one memory of a store brand not being the same quality as the name brand. My girlfriend told me that the store brand Mac and Cheese was bad. So, for two people, I only know of two times the store brand was not up to par. In my case, I got a full refund under the company quality guarantee.
When you think about it, it is usually only a quarter or a dollar. Over time, it ads up quickly. You have to pick which products you will not budge on, but for most things you buy, you can probably save a lot. I will never give up my Tropicana orange juice, or Crest Toothpaste, for example. For the most part, though, I would rather give away less of my money for the same thing.