As in 'digital' circuits, you just need to break the circuit and interrupt the flow of charge. In theory, you could break either leg. In practice, it's better to break the 'hot' leg, just in case someone/thing accidentally grounds out part of the circuit/case that is still hot, or cuts the cable, or some such.
Most power relays can do the trick, as long as the 120V doesn't arc across the contacts (as may be the case when the contact and paddle/reed are particularly close together, as may be the case with low voltage relays). If there's an AC rating for the contacts, it should do the trick. Obviously, the coil must be rated for 24V (AC or DC, you don't specify).