Officially, not always. They usually only allow service animals inside. Home Depot requires that service dogs be on a leash at all times while you shop in their stores. Service dogs are dogs that are specially trained to assist people who are disabled, be it physically o mentally. This includes military veterans with PTSD.
So, this is a pretty clear cut answer that you should not bring your dog inside a Home Depot, if you're a regular pet owner. If you really want to take the pooch to Home Depot with you, though, it's best to contact the store manager ahead of time. Some stores are very loose about their dog policies, so they may still let you in.