From a religious standpoint, I believe God put animals on the earth for us to use as we need to survive. That being said, They shouldn't be treated poorly, Unnecessary suffering in any sense is wrong. They should be used only for survival purposes (including scientific testing) and in some cases can be kept in captivity but only if treated well.
If by "use" you mean use them for medical experiments, Test cosmetics on them and use them as performers in circuses and at Sea World, Then no, We have no right to use animals as we want. It's inhumane. How would you feel if you were stuck in a medical lab and experimented on or trapped in a metal bathtub away from your family and forced to perform tricks?