Species differences are important
The straightforward answer to this question is NO. You should NEVER give a human drug to your pet animal unless your veterinarian advises you to do so ! Of course most drugs that are prescribed for animals by veterinarians are the same (or similar) drugs that physicians prescribe for human ailments - but there are huge differences in the way that different species species of animal deal with a drug once it is their system. So, some drugs that are safe to use in humans are positively dangerous to give to pets and other animals.
A well known example of this is aspirin, which if given at human dose rates, can easily cause toxicity in both dogs and cats because they cannot detoxify and eliminate it from their bodies as quickly as humans can. The result is a severe gastroenteritis - which may cause them to vomit blood.
There are literally hundreds of examples of human prescription drugs which can cause toxicity to dogs, cats or other pets. Other common medicines and so called social "drugs" which definitely should not be given by owners to their pets are :
All of the above have been documented to cause serious illness - and are potentially fatal . The message is - NEVER assume what is safe for you and your children is safe for your pet - the chances are it isn't.
Updated October 2013