The duvernoy's gland in garter snakes produces a true venom, but not in huge quantities, nor of extremely high toxicity (though some vipers have very similar venom). However, it can't enter your bloodstream in any quantity that would cause a reaction unless they really chew on you for a long time, and work it in with their teeth. Most people don't let a snake keep chewing on them for an hour. 
Some people can, of course, develop an allergy to venom. In that case, even a small amount could cause a serious reaction. Folks who are allergic to bee stings would be particularly at risk for this.
People with serious venom allergies should probably not keep garters, water snakes, or hognosed snakes, and certainly not rear-fanged species. (Hogs aren't true rear-fangs...their fangs are designed to pop holes in toads to let the air out, not to channel venom into their prey).