Steel is what the original bike was made out of. And steel is still the most popular frame-building material. If your bike is from K-Mart or Target, the frame is pretty much just sections of thin-wall pipe welded together. As you spend more $ and upgrade, you get better material, and better manufacturing and construction techniques.
There are a lot of alternatives to steel in the 21st century. Aluminum is popular. At the higher end, frames are constructed of titanium, carbon fiber, etc.
I've attached some photos of truly-exotic bicycle frames. One is bamboo. (Actually rather ingenious - it's organic, but it's strong and lightweight, and its fibrous composition gives it a lot in common with oriented carbon fiber.) The other is wood. It's Clancy's homemade wooden bicycle. He built it himself, and I am totally impressed! You may see him riding it, on the streets of Boise. (It looks a little heavier than some of the bikes out there. And I've told him he needs to be careful on windy days... a sudden side-gust could send him airborne. But it is beautiful, functional, and ingenious.)
If you're interested, there's an article about bike frames on the Wikipedia. (I'm cautious about using the Wikipedia when I'm looking up information that's disputed. But bike frames aren't that controversial, huh?)