Pros: Nonreactive (meaning you can cook any kind of food in it), heavy, durable, dishwasher-safe, inexpensive for basic models. Cons: Poor heat transfer and distribution.
Pros: Excellent thermal conductivity, cooks food evenly. Cons: Reactive with alkaline or acidic foods, which can take on a metallic taste after being cooked in a copper pot.
Pros: Excellent thermal conductivity, lightweight, affordable. Best for backcountry use. Cons: Like copper, raw aluminum is highly reactive to alkaline or acidic foods.
Pros: Durable, inexpensive, naturally non-stick if properly seasoned, distributes heat evenly and retains heat well, imparts iron to foods (an added benefit for some), great for long, low simmering and browning. Cons: Cast iron is also reactive, and doesn't take well to acidic foods. It's also quite heavy, takes a long time to heat up, takes a bit more effort to clean and maintain.
Pros: ideal for boiling water because they can be made with very thin walls, and transfer heat efficiently. Cons: like stainless steel pots, they tend to develop hot spots, making them less than ideal for cooking real meals.