While there are numerous exotic animals (kangaroos, ostriches, eels) that make perfectly good jackets, you’re probably going to encounter a few more common breeds of leather. There are benefits and drawbacks to every type.
Cowhide: Today, it's the most common leather used in the construction of jackets. It's tough (though not quite as rugged as horsehide) but becomes supple over time. Cheaper than horsehide, variations include the slightly pricier steerhide and the tough-as-nails bullhide. Unless you're out on the range or plan to wear your jacket while working construction, this should work for you.
Horsehide: In postwar America, horses did the major share of agricultural work, which meant the skins of these beasts were the go-to material used in leather jackets. While horsehide has become less common these days, it remains one of the toughest leathers you can buy. Because of that resilience, horsehide jackets can be difficult to break in and uncomfortable to wear at first. However, the material provides almost unparalleled protection – perfect if your ideal leather jacket accessory is a Harley Davidson.
Goatskin: Softer and more flexible than cowhide, goatskin guarantees that your jacket will weather and age extremely well – it's one of those rare leathers that actually looks better the more you beat it up. With a characteristic pebble grain, it's also the go-to leather used by the Air Force and Navy for their A-2 and G-1 flight jackets, making it perfect if you're trying to get some runway cred.
Calfskin: Soft and pricey, calfskin leather is characterized by a fine grain, but it's still fairly durable and does not easily show scratches and blemishes. Typically used to construct shoes, calfskin jackets are far less common that they are versatile. They provide warmth in cold weather while still being lightweight enough to wear comfortably on a brisk spring day.
Lambskin: Lambskin is smoother than butter and about as durable as a china cup. Extraordinarily lightweight and comfortable, it tends to be expensive and is prone to tearing. Still, jackets made from lambskin are substantial enough to wear all year long, provided you don't plan on going into a controlled slide.