Quoted from cfh:

If it's a DC powered coil, it needs a diode. (This included EM games that use DC power for the pop bumpers, though Williams sometimes didn't do this initially, though bally always did.)
after a coil is powered, and then the power is removed, it creates a backwards surge at twice the powering voltage. The diode shuns this voltage from going back and damaging components. On a solidstate game, a coil with no diode usually smokes its driving transistor after the first energize.
the problem with coils and diodes is, you have to hook up the coil correctly. that is, the power lead (on a two lug coil) goes to the banded diode coil lug. If these leads are reversed, usually the coil diode shorts and/or the driving transistor shorts (on the driver board.)
because this was such a problem, starting around system11b, williams tried to move all the coil diodes to the auxilary power board (not flipper coils though.) this would allow an operator to install a replacement coil without concern with which wire goes to which coil lug. this thinking also wrapped into WPC games too. But by pinball 2000, williams changed their mind on this, and coil diodes came back.
On williams/bally sys11b (and newer) and wpc games with the coil diodes mounted remotely, it never hurts to have a diode on the coil too. Just you have to hook up the coil wire correctly.

Quoted from wellarmed:

If your machine is a roadshow then there should not be a diode on the coil .
If your old coil was toasted then is probably the driver toasted too .
Cut the diode out and power the machine on , if the coil fires up then the driver needs to be replaced .