Usually when choosing cookware you are concerned about how well it conducts heat, and how evenly it conducts heat. The normal concerns are to ensure that heat is distributed evenly and efficiently allowing you to cook as quickly and consistently as possible.
When considering cookware for an induction cooktop there is an extra concern - will it work on the cooktop at all? Put a glass pan on an induction cooktop and it will not heat up at all. A review of cookware brands can be found here. I have tried to answer the 'will it work' question on a brand by brand basis but, for in case your brand is not mentioned, we need to conside the actual material the cookware is made from.
As we saw on the technology page, induction cooktops do not generate any heatr at all. Rather, they produce a magnetic field just above the glass. As long as the base of the pans you use is ferrous (based on iron) the pans should work. The simplest test is to see if a magnet will stick to the base of your pans. If it sticks, cook away. If not, you need a different set of pans or a different cooktop.
Most stainless steel pans will work on an induction cooktop BUT some types of stainless steel will not work at all, while others will heat very slowly. If in doubt about your pans, try the magnet test.
So what is all this about 18/10 or 18/0 stainless steel? The 18/10 refers to the proportion of chromium to nickel in the stainless steel alloy. To be classified as stainless steel, an iron base alloy must contain at least 10.5 % of chromium. The presence of chromium enables the steel to form an invisible layer of oxide that protects it against corrosion. If this layer is damaged, a new one forms immediately due to the oxygen content of the air. Increasing the chromium content to 18% has further increased this protection. The addition of nickel to the alloy increased its corrosion resistance while adding a bright polished appearance, hardness, and exceptional resistance to all temperatures. As the nickel level is increased, the quality of the stainless steel is increased. The “top of the line” boast 10% nickel content, the highest quality available in stainless steel.
And how about tri-ply? What is that? A try ply bottom ensures superb heat conductivity for rapid, even cooking. The nest tri-ply has a layer of aluminum sandwiched between two layers of 18/10 stainless. Stainless steel alone is not an effective conductor of heat whilst aluminum readily absorbs heat. By absorbing heat faster than the neighboring stainless steel, it can provide even heat distribution before heat is transferred to the food. The end result - faster more thorough cooking without cold spots or hot spots. None of this detail about stainless steeel changes the basic test for induction compatibilility - if in doubt about your pans, try the magnet test. If the magnet sticks to the base of the pan, the pan should work on an induction cooktop.
Cast Iron Cookware
Cast iron cookware should work very well on an induction cooktop.
Aluminum (or, for the English readers, aluminium) and hard anodized aluminum
Aluminum pans will not work at all on induction cookptops. Aluminum is a non ferrrous metal and is not magnetic. Do not discount composite pans howerver - there may be layers of aluminum and stainless steel sandwiched together. Again, try the magnet test
Although copper is the best conductot of heat, it is not a ferrous metal and as a general rule, will not work on an induction cooktop.
Glass pans will not work at all on induction cookptops.
Non stick pans are made of metal and coated in a non stick surface. It will depened on the underlying metal whether they work. If in doubt, try the magnet test.
Remember - don't ever assume something isn't hot or won't get hot. If in doubt, test it!