Traditionally, blacksmiths worked with iron (of course). The iron that would, eventually, typically be used was known as wrought iron. Essentially wrought iron was just iron that had been worked after it had been smelted in a foundry of some sort in order to improve its qualities. As a matter of fact, "wrought" just means "worked". All in all, it was pretty enduring stuff, easily workable (relatively), and had a interesting grain to it, almost looking like wood. These days, wrought iron is awfully rare and quite expensive. The reason for this is that most steel mills these days don't bother making wrought iron and those that do tend to only produce it for custom orders.
Instead the vast majority of modern ornamental iron work is done with mild steel. While this metal is significantly cheaper and has some desirable qualities over wrought iron, primarily composition consistency, it does not have the corrosion resistance. Word of caution: the term wrought iron is now widely overused and greatly misused. Remember that "wood grain" evident in wrought iron? The next time that you look at purchasing something claiming to be made of it, take a look and you ought to be something that looks like layers and layers forming a wood-like texture.
For those of you looking to get started in smithing, I highly recommend starting with mild steel. All in all, it is pretty forgiving for the inevitable mistakes that you will make on your road to mastering your skills. Just make sure if you buy something from a hardware store you don't buy anything that has been galvanized! Metal fume fever is absolutely no fun! The effects are temporary, but those hours will pass very slowly. Most welding rods are just fine for practice and ornamental work and, as mentioned earlier, they are pretty inexpensive since mild steel is produced on a massive scale and has a great number of applications.
Spend some time (as in one heck of a lot) working with this steel before you move on to higher grades, like the many types of high carbon steel. The hammer skills you develop and base understanding of steel will serve you greatly in the days to come. You don't want to rush yourself when it comes to blacksmithing - that's a good way to get hurt, damage your tools and equipment, or ruin your projects.
When you do venture into the complex world of high carbon steels, be prepared to do some research. Depending on what you will be making, you will want to consider the properties of various alloys. Always be familiar with the steel you chose and what can be expected of it, not to mention its limitations. You don't want to have your steel crack under your hammer blows or break apart in the forge because you got it too hot (I'm looking at you, stainless steel!). There is nothing more frustrating than being almost finished with a project only to have it be rendered useless because you pushed the metal beyond its limits.
I know, I know, research doesn't sound like a lot of fun, but you will be thankful for it in the end. Many engineering and trade books cover the many types of steel available and their properties in great deal... perhaps too great of detail. For those just getting started, and without high level metallurgy knowledge, read up on blacksmithing books (The Complete Bladesmith by Jim Hrisoulas is a good choice, especially if you plan on making knives one day) and even the blacksmith forums.
Time to get to work!