Different Steels
Stainless:
The exact definition of when steel becomes "stainless" is not rigidly defined, but most describe any steel with more than 13% chromium in it as "stainless". Of course, steels aren't completely stainless -- they will rust if given the chance -- but stainless steels resist rust much longer by virtue of their high chromium content. Many stainless steels are used for cutlery. The low-carbon high-chromium steels, such as the 3xx series and 420 stainless are usually seen in applications such as dive knives, where rust resistance is much more important than edge holding. The next step up in edge holding is to go to steels with more carbon, such as 425M, 12C27, 440A, and AUS-6. As you go up in carbon, you are getting less rust resistance, but typically you're adding hardenability and thus edge holding. We can step up again to GIN-1, 440-B, 440-C, and AUS-8. AUS-10, ATS-34, ATS-55, and 154-CM have better edge holding still. Some steels that aren't seen as often but show great promise are BG-42 (close to ATS-34 but with added vanadium) and CPM's 440V and 420V steels. All those steels have excellent edge holding, with 440V and 420V being just incredible.
Non-Stainless (carbon and alloy steels):
There are a wide variety of non-stainless steels used in knifemaking. These steels do not focus their alloy mix on being rust-resistant, which means they are instead focussed on edge retention, superior toughness, or both. As a result, provided you're willing to put up with a little extra maintenance, you can see great performance results with these steels. Among the steels you'll see are the 10-series (1095 for knives, 1084, 1070, 1060, 1050 for swords), O-1, W-2, A-2, L-6, D-2, and 5160. You'll also see the great edge holding 52100 steel, in knives made by those who forge their steel.
Damascus:
Damascus is made from two or more metals welded together. Most Damascus has a striking beauty, obtained when the final product is acid etched. The two different metals in the Damascus etch at a different rate, leaving a striking pattern. Much Damascus is forged strictly with the objective of obtaining a beautiful pattern. However, there are many makers forging Damascus with an eye towards performance. Such Damascus might be made from O-1 and L-6, for example. Stainless Damascus has also become available
.
Non-steels Used For Knives:
A number of materials are used to replace steel in knife blades, with varying success. At the lowest end are the cheap CIA Letter Openers, with zytel-like blades. These knives aren't really a serious contender against steel, performance-wise. Some of the tough high-tech handle materials, like G-10 and carbon fiber, are being used in knives today. They don't take an edge like steel, but are completely undetectable and non-magnetic, and some can make passable last-ditch weapons. Some makers are binding a very thin layer of steel to thicker layers of carbon fiber. The steel provides a working edge and the carbon fiber reinforces the steel for strength. The knife remains very lightweight due to the small amount of metal used, but the edge remains steel and so performs better than a synthetic edge. Several manufacturers and makers are using ceramic composites. Their primary benefits are that they hold an edge much longer than any steel, and that they are completely non-corrosive. On the down side, they are much more brittle than steel. The worst of them can easily break by just a small drop to a hard table; however, the best of the ceramics is reasonably tough, tough enough for hard chopping and the like. Cobalt-based alloys also show a lot of promise. They hold an edge for a very long time, and non-corrosive, and are much tougher than ceramics. These alloys -- such as Stellite 6K, Boye Dendridic Cobalt, and Talonite -- are much more expensive to work than steel, but tests are showing excellent results. Titanium is also used as a blade material. Non-corrosive and much lighter than steel, it can take a reasonable edge and holds it okay. The best titanium alloys vastly overshadow the cheaper titanium alloys in inexpensive dive knives.