I'm with @Ward -- I like being able to scour my pans for those times when even deglazing doesn't work. (although, I've found that if you ever forget about the stock that you're trying to reduce ... burning chicken bones is a nasty smell and will stain even stainless steel).
I do have some non-stick, and even a non-stick flat-bottomed wok (from circulon, but then, I'm also using electric, so it's possible I don't get enough heat to ruin it; I also never pre-heat it without oil in it, as you should never heat a dry nonstick vessel).
I'd say to look at replacing your set bit by bit -- which items do you cook that really need non-stick, and what pan do you cook it in? Maybe replace your more beat-up items with something not non-stick, try cooking with it, and see how well you like cooking with them -- it's possible that you won't like it, and it'd be better to be out the cost of only a piece or two than a whole set. You could even try out a few different materials -- cast iron, stainless, anodized aluminum, etc.
It also might take a little time to get used to cooking with out the non-stick. One mistake I've seen people make is not giving their pans enough time to pre-heat. (I think it was the Frugal Gourmet who'd say "Hot pan, cold food, food won't stick" ... which isn't entirely true, but you'll have much less problems with a hot pan).
If a magnet sticks to it, it's ferrous.
I'd like to give a more elaborate answer, but there isn't anything more to it.
Best Answer
I second Joe's advice.
Your pans may be too thin, that would make your dishes burn easily. You can test your pans with a simple experiment. Place a thin layer of water in your pan (an eighth of an inch, or just enough to cover the bottom). Turn on your burner to high. If you have an electric stovetop let the burner glow before placing the pan on the burner. Watch how the bubbles form in the pan. If they are uneven over the bottom, you have hot spots.
This photo is actually uneven heating from the burner, not from a bad pan, but it shows the idea:
you have hot spots.
If your pans have hot spots you need to stir more often and maybe lower the heat from what the recipe calls. Pans with thicker bottoms and made with good electric conductors (copper or aluminum) have fewer hot spots.
Then there is what I call the Remick Maxim. Three years ago when I decided I would learn to cook better, I went through many cookbooks and asked a lot of people for advice. A great friend (a French restaurant level cook) told me the best advice he ever got was from the actress Lee Remick, a good cook herself. She said: “the secret to great food is to cook it in low heat.” Best advice I got on cooking.