The vast majority of animals, and certainly all larger animals have red blood similar to our own. There are popular misconceptions about the color of animals blood that a lot of them have different colored blood to us. In reality this is only a very small portion of all the animals in the world, and most certainly have red blood. They have hemoglobin in their blood, just as humans do, which contains iron, which gives it its red coloration.
While all mammals and larger animals have red blood, there are a few animals, mainly amphibians and lizards that have greenish blood as well. This is because their blood contains bile making them poisonous to most predators. Whether this is a way of avoiding predators or simply an easier way to expel waste that gets built up in the body isn't known.
There is also a popular misconception that animals and humans blood can be blue until it makes contact with the air, where upon it becomes red. There is some slight truth to this however. Some animals such as crabs and lobsters use copper rather then iron as the main component of their blood cells. This gives their blood a blue color as their cells contain hemocyanin rather then hemoglobin as ours do.
Because copper isn't very efficient at binding with oxygen in the blood. The blood of crabs and lobsters usually has a faint shade, rather then the rich shade of red that our blood has. This is because it contains less oxygen. Lobsters in particular have poor oxygen absorption, and may have almost gray blood in some cases. Human blood by contrast as with most mammals is very oxygen rich. Because we expend a lot of energy moving and keeping warm, and so use up more oxygen.
Smaller creatures such as insects van have a multitude of different colors as their blood color. Things such as beetles, or caterpillars for example often have yellow colored blood. This is because they use a different system for binding oxygen to humans and larger animals. Where we use hemoglobin and iron to bind and absorb oxygen, they tend to use Hemolymph. This isn't strictly the same as blood but serves much the same purpose, and contains all the chemicals that they need to breathe and survive.
In some insects such as this their blood isn't even pumped around their body, rather it is free moving and moves as their bodies move. To allow them to still receive oxygen though they can usually breathe through their skin all over the surface of their bodies. Thus ensuring that enough oxygen still passes through to all their organs.