Curse is an interesting move, since now anything that learns it can benefit from the Ghost mechanics. Magic Guard won't care, and of course the target can just switch, but it's a good way to shuffle the team or stop a sweeper from going crazy. Here are a few mons that might do well with the move. All are assumed to be the Ghost type with additional dual-types listed.
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Ghost pairs well defensively with those 4 types, so you can add whatever synergizes best with your team. The Slowbros are unique in that they can abuse Curse and Regenerator, which lessens the HP loss from the move. Tangrowth can also learn Curse from a Gen I TM, but I think it's illegal with Regenerator. Anyway, once you Curse something, you can use the next turn to Yawn, switch and regain HP, or status with T-wave or Toxic. They aren't very threatening offensively, but if you run Ghost/Dark, you can gain STAB on Foul Play and do some decent damage assuming the incoming target is invested in Attack.
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A faster, more offensive approach can work with Aerodactyl, though it struggles to perform the following roles simultaneously without becoming overburdened. After it Curses, or even before, Aero can use Taunt to stop any healing hijinks. Roost is optional and recommended to heal itself the loss of HP. Then it has one slot leftover to do some damage. Normal is listed to gain STAB on Rock Head Double-edge, though in a meta filled with lots of Steel and Ghost-types, it probably isn't as useful. Ground is there to get the boost on EQ; against non-Levitate Steels, it will do a fair amount of damage. Dark is listed should you want to mega evolve and gain Tough Claw boosted Crunches, which are handy for hitting Normal/Ghost combos. Since it really only has one slot to attack, however, Aero is easily played around.
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Avalugg is probably the most defensive of these sets and can take on most physical attackers with ease. A Curse set might seem counter-intuitive when it wants its HP preserved, but it has tremendous bulk and instant recovery, so it can usually live an attack even with only 50% HP left. Ghost/Normal is there to absorb other Ghost attacks. The weakness to Knock Off is mitigated, again, by its insane Defense. Steel typing can power up Gyro Ball, gives it some nice resistances, and means it doesn't fear Toxic anymore. Ground powers up EQ. With Curse, it probably won't have enough time to Rapid Spin, a niche it can retain with other sets. Roar becomes pointless, unless of course you use it on a target you haven't Cursed.
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Magic Bounce is a really nice ability in such a stally metagame. It means Absol can't be Taunted when it wants to use Curse, and it can't be worn down with Toxic or Will-O-Wisp in between Curse and Wish. The Dark-typing is added (or retained, technically) to keep STAB on Knock Off, a good move to pair with the switching you'll induce. Taunt can also be added for stopping the opponent from healing itself. Mean Look helps trap any non-Ghosties (you'll be Knocking Off Shed Shell from other types) and Perish Song can increase the annoyance even further. Have fun with this one!