It depends. Many factors—your style of riding, your weight, your sense of adventure—all play a role in your choice of material. The following paragraphs explain the different types of material commonly used on bikes. A few bikes out there are made of exotic metals, but that's another discussion entirely.
Carbon (High-Tensile) Steel
Steel is the most commonly used material in bike frames. Carbon or high-tensile steel is a good, strong, long-lasting steel, but it isn't as light as its more high-tech brother, the steel known as chromoly.
Chromoly (Chrome Molybdenum) Steel
A workhorse of the industry, chromoly is a light, strong steel. When it is butted and shaped to take off excess weight, it can deliver a fairly light frame that will last through years of hard use. Chromoly is responsive and offers good flex while maintaining its form.
Having come a long way from the oversized tubes of old, aluminum is now less expensive and very widely used on today's bikes. It's light, strong and stiff. With proper design it can give a solid ride for climbing, or lively handling in tight situations.
Lighter than steel but just as strong, this more-expensive metal is found on high-end road or cross-country mountain bikes. It flexes so well while maintaining its shape that some very high-end bikes use the metal itself as a shock absorber.
Take a bundle of parallel continuous fibers and bind them together with glue. This creates a ply. Several plies are made up to form a laminate (just like plywood). And the laminate, if designed right, can be very tough. It's also light. So why aren't all bikes made out of carbon fiber? It tends to be brittle. The fact that metal can bend and regain its shape is what makes it last. Because of this, carbon fiber bikes are built even stronger than needed.