Good question, Michelle. Garlic does have toxic potential to pets, and is generally more potent than onion, also a member of the Allium species, in causing changes in red blood cells in dogs and cats. This is true in raw, cooked or powdered forms. In theory, "deodorized" garlic is allegedly less toxic, since the disulfides, responsible for both the odor and the toxicity, are usually largely removed.
Even at low levels of exposure to garlic, some change in red blood cells is likely; it is typically only when a significant number of red blood cells are altered that their oxygen-carrying capacity is noticeably compromised and clinical signs develop. Generally, it takes either a fairly large single ingestion or chronic exposure. These effects are also somewhat more likely to be seen in cats, as their red blood cells have shorter life spans and they're more likely to have bone marrow issues. However, the possibility exists that some dogs may also be genetically more susceptible to problems from garlic ingestions.
The lowest observed effect level in dogs in the scientific literature that we are aware of is 2.5 mg/kg of encapsulated garlic powder; slow heart rates and increased urination were seen. For comparison, a 20-pound dog consuming 1000 mg of garlic powder is exposed to a dose of 110 mg/kg.
The bottom line, Michelle, is that we do not definitively know at what dose any given dog may experience problems. An occasional low dose, such as those found in most commercial pet foods or treats, would not likely cause problems. A conservative approach might be to avoid exposure to more concentrated garlic-based products.