According to Modern Dog, it is acceptable to give dogs a little tuna or some water from canned tuna. The liquid is also a useful ingredient for homemade dog cookies. Australia's RSPCA indicates that tuna is fine as an occasional treat but shouldn't be offered on a daily basis.
Modern Dog also suggests that cooked herring is beneficial to dogs. This fish contains essential fatty acids that help keep skin and coats healthy. In addition, the fats are thought to be useful for dogs with arthritis.
WebMD warns against giving dogs raw fish, because it occasionally contains bacteria that cause food poisoning. Uncooked salmon, trout, shad or sturgeon sometimes carry deadly parasites, as well.