A dark and horrible curse that, as a side effect, gives you a variety of cool superheroic powers. Vampirism, lycanthropy, deals with the devil, etc. But it's a little problematic when the coolness of the powers overwhelms the price. People gloss over the "having to drink blood" thing and focus on leaping tall buildings and turning into ninja bats.
Looking specifically at games, one of the contributing factors is that players tend to be given a shopping list of cool powers to choose from. More text-space (and hence brain-space) is given over to the upside. And when your choice of powers is how you customise your character, it's natural that they're the aspect you focus on.
Of course when I put it like that, the solution seems obvious. Swap it around. The cool powers are defaults, and the price is unique. Thing is, cool powers that aren't diverse aren't terribly cool. If you can do something the other person can't, then that makes you cooler when you do that thing.
Fortunately the game that had me thinking about this problem already has an answer to that. Classes - broad categories of character concept and abilities. The difference will just be that classes don't come with a selection of bonus powers, but with your choice of horrible drawback.
For example: you're a swordbearer - you have a demonic soul-eating sword bound to you. Traditionally you'd be able to customise your sword so that maybe it could shoot fire blasts, or had a big glowing eye that warned you of threats. But I think it'll be more interesting and appropriate if the cool powers are relatively generic (though you can justify the colour/flavour to suit your tastes) but the drawback is specific.
To continue the example, maybe the demon sword is a deep sleeper and you don't benefit from any of the upsides until it's been woken up by tasting first blood. Or it's a monstrous organic parasite that drains your strength.
To sum up: keep the cool powers broad, the drawbacks specific and let the player customise with their choice of drawback. It might work.