I knew there was a lot of different styles of jeans, whereas the straight leg was probably the first and most common, but I could find twelve others. I'm sure there's many more, and variations on some of them. Here's the twelve I could find:
Baggy/Loose - "Baggy was a British dance-oriented music genre popular in the early 1990s. The scene was named after the loose-fitting clothing worn by the bands and fans."
Bell-bottoms/Bootcut/Flair/Hip-huggers - "Bell-bottoms are trousers that become wider from the knees downwards. Related styles include flare, loon pants and boot-cut/leg trousers. Hip-huggers are bell-bottomed, flare, or boot-cut pants that are fitted tightly around the hips and thighs worn by men and women."
Boyfriend - "In fashion design, primarily in ready-to-wear lines, boyfriend is any style for women's clothing that was modified from a corresponding men's garment. Examples include boyfriend jackets and boyfriend jeans, which are more unisex in appearance than most women's jackets or trousers while they are still designed for the female form."
Carpenter - "Carpenter jeans are jeans with many pockets and loops which can be used to carry objects such as tools and are often loose around the leg to be able to accommodated the affixed items."
Skinny/Slim-fit/Drainpipes - "Slim-fit pants or skinny jeans have a snug fit through the legs and end in a small leg opening. Other names for this style include carrot leg pants, cigarette pants, drainpipes, peg leg pants, pencil pants, skinny pants, slimjims, tapered pants, or ice-cream cone pants. Skinny jeans taper completely at the bottom of the leg, whereas drainpipe jeans are skinny but then the lower leg is straight instead of tapering and so they are often slightly baggier at the bottom of the leg than skinny jeans. In some styles, zippers are needed at the bottom of the leg to facilitate pulling them over the feet. Skinny jeans are worn by men and women."
Wide leg - "Wide leg jeans are a style of clothing popularized in the mid-to-late 1990s, especially by men trying to achieve an "alternative" style. For men, the style is also called hip-hop clothing and remains popular with this subculture in 2008. The quintessential brand of 'hip-hop' style wide leg jeans was JNCO, though other youth and ethnic oriented clothing companies manufacture them as well."