Southwest Airlines specifically bans self-defense type sprays on all flights, both in checked and carry-on luggage. Other Southwest Airlines restrictions on luggage reflect the rules of the Transportation Security Administration, and are often dependent on whether the luggage is carried on or checked.
The TSA allows some items in checked, but not in carry-on luggage. These largely include items that could potentially be used as weapons. Sharp items such as knives, meat cleavers, scissors, ice picks and box cutters are only allowed in checked luggage. Tools such as axes and hatchets, cattle prods, crowbars, hammers, drills, saws and other tools that are longer than seven inches must be packed in checked luggage. Sporting goods such as baseball bats, hockey sticks, lacrosse sticks, golf clubs, spear guns and ski poles are also allowed in checked luggage only.
There are many items that are banned outright by the TSA, in all types of luggage. Gasoline, larger quantities of aerosol, lighter fluid, explosive materials and realistic replicas of explosives, chlorine, liquid bleach and strike-anywhere matches are all examples of items disallowed in checked or carry-on luggage. The TSA provides a full list of specific items banned from carry-on luggage and checked luggage at their official site.