Steel is Real
Chrome-moly steel is very popular for bike frames. 4130 chrome-moly steel alloy is one of the most popular alloys in the bike industry, and is renowned for stiffness, damping and durability. Steel can also be repaired easily in the event of a crash. Stainless steel is used frequently in bike components, from bolts to chainrings, and makes a good choice for nearly every metal component of a bike. There's a weight tradeoff using steel, but it's more durable than aluminum and a lot less expensive than titanium or carbon fiber.
Light and Stiff
Aluminum is a lightweight metal that is used most frequently in components like wheels, handlebars, chainrings, and seat posts. Aluminum is a softer metal, but has an extremely good strength to weight ratio that makes it ideal for almost any cycling application. Aluminum rims also provide a much safer braking surface than steel rims, which are no longer made due to poor performance in wet conditions. Aluminum doesn't rust, but is subject to corrosion.
Cream of the Crop
High-end bicycles can be made from extraordinarily light and stiff materials at a premium price. Titanium alloy is difficult to weld and manufacture, but the extremely hard metal makes for very light bicycle frames and components that are completely resistant to corrosion, even after decades of hard use. Carbon Fiber, a material made from laminated strips of carbon strands sandwiched together using a resin, is also difficult to manufacture, but offers unparalleled stiffness and light weight. Carbon fiber bicycles are ubiquitous at the top levels of competition for nearly every cycling discipline.
Other materials are essential for the construction of a bicycle. The vulcanized rubber used in tires and brake pads won't crack or stiffen in cold temperatures, giving it exceptional resiliency for hard use. Leather, synthetic fabrics, and even foam and gel composites make their way into everything from seats to grips to tires, and offer flexibility and comfort for the contact points of a bicycle. Even plastic can often find purpose in some bicycle components like seats, valve caps, grips and shifters. Creative bicycle designers often experiment with other materials like wood and plastics to push the boundaries of material use in the cycling world.