Actually, some boards (such as the Capcom CPS-3) can output S-Video or Composite video. If this is the case, a TV can be used.
If you are in europe, you can connect the RGB out from a JAMMA connector to a TV with SCART in. SCART TVs are not easy to get in the USA or other parts of the world.
If your board only has RGB out, and you cannot get a SCART TV, you would need a converter than can convert the RGB to an input your TV has, such as Component, S-Video, Composite, or RF. Note that a TV will display lower video quality than the original arcade monitor when this method is used.