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).
A regular electric oven uses a large coiled resistor as a heating element. A large electric current is passed through this element which generates heat, similar to the tungsten filament of an incandescent light bulb.
An induction stove doesn't actually generate heat itself, but rather induces it the pot or pan. It does this using a rapidly oscillating magnetic field. This field induces an electric current in a ferromagnetic pan which generates heat, thus heating the food.
Induction stoves are faster, safer, and more energy efficient than traditional electric stoves. It requires significantly less electricity to create the magnetic field than it does to drive enough current through a resistor to make it heat up. They are safer because they don't actually generate heat themselves. After taking a pot off the "burner" (glass surface) it quickly begins to cool.
With regards to differences in the cooking process, there's not much. You just need to be aware that it heats up much more quickly and cools down much more quickly than a traditional electric stove. It does affect your choice of pans however. All aluminum pans will not work, nor will some lower quality stainless steel ones. If a magnet sticks to the pan then it will work just fine. The pan must also have a flat bottom to make full contact with the surface.
Best Answer
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.