In general, we do not recommend using any human medications in your pets unless first consulting with your veterinarian. Unfortunately, we have had many instances where pets have been harmed by people with good intentions having given them a medication that they may take themselves for a similar ailment. There are many over-the-counter medications that can be toxic to dogs and/or cats. For example, Tylenol (acetaminophen) can be lethal to cats because they lack the appropriate liver functions needed to process the product appropriately. Pain medications in the nonsteroidal anti-inflammatory category such as Advil and Aleve can be especially hard on dogs' and cats' stomach and kidneys. In addition, if one of these medications has been given, it greatly limits what medications the veterinarian can then safely prescribe. This is because of extended "washout" periods that are necessary to avoid harmful interactions these medications can have with other drugs.
Some medications may not necessarily be harmful, but might not help when others might be more appropriate. People often reach for antihistamines such as Benedryl or Zyrtec to help with a pet's allergies. In reality, an extremely small percentage of pets respond favorably to these medications. If they are extremely itchy or have a significant amount of skin irritation, these medications just aren't usually enough, and attempts to use them merely delay getting the pet something that might really help the situation.
Topical products might also be harmful to pets. Antiseptics such as hydrogen peroxide or rubbing alcohol are not recommended and can cause more irritation to a wound if used for the purpose of cleaning or disinfecting. Over the counter eye drops such as Visine, can be similarly irritating.
There are certainly some human medications that we might suggest for certain situations. Often this is when a safe species-specific product is not available for a particular use. A general rule of thumb is to always consult your veterinarian prior to administering or using any human medication in your pet.