Powers have the potential to over balance a story. Let us create a hero. He is invulnerable, super strong, and super fast. This is a hero that is a living tank. If he is in a story that is all about fighting, he will do fine. He will win simply by being able to out last and out smash every opponent. This is the story for a child, with no depth. Once this same hero starts facing personal and/or ethical dilemmas the hero will either be forced to change, or to fail.
For example. (Hero) takes on heavily armed bank robbers. Bank robbers thought the had a plan to beat (hero) and came armed for a heavy battle. By the time the fight is over, the bank is trashed, and so are several cars outside. There were grenades, rockets, and high powered guns with armor piercing ammunition. In a city, this all adds up to collateral damages and casualties. (Hero) now either smiles for the camera, waves, and flies off into the sunset until the next episode, or he tries to help out with the clean-up, and is forced to see the injured and dead among the damaged buildings and cars.
The difficulties for the writer depend on how deep they want to go into the world they are creating. One of the biggest challenges for a writer is that the more super-human a character is, the harder it can be to keep the hero human at all. There must be some kind of acceptable grounding of the character in the same reality that everybody else faces.
Story-telling with powered characters let the story-teller work squarely in fantasy. Rules can be slightly bent because the audience has already agreed to suspend realism. The difficulties lie in making sure the protagonist's challenges are still accessible to the audience. If nothing is accessible to them, they probably won't get invested in seeing the ending. It is also possible to bend the reality of the story-world too far. When this happens it distracts the audience and confuses them. A confused audience also won't care about the ending.
I personally can't think of a 'good or bad' set of powers. Some might be more difficult to pull off and require a different 'tone' of story, but I think just about anything can become a story that some audience will enjoy. Of course, I've no professional experience in the publishing field, so I speak naively.
Powers add another layer to the storyline, allow for an easy path to conflict/change, and also give pretty awesome action scenes to boot. However, with every power, the author must be careful so it doesn't instantly solve the setting's woes in three minutes. Furthermore, they would want to avoid anything that's too generic/done before. So, good powers are things that aren't too powerful and are interesting (i.e. bug control, ability to extrapolate information from almost nothing, darkness generations, ability to be forgotten/ignored etc.) while bad powers are powers that are too powerful to realistically explain why they haven't either fixed all the problems for all time, or decided to turn the world into their plaything (i.e. Post-Panacea Khepri, Superman). These also remove conflict, and with it any and all tension and drama that could be in the story. The exception, of course, is that bad powers are only bad in the pure power-aspect. If politics are in play (i.e. Worm, Strong Female Protagonist) then the conflict is derived less from powers, and more from the deconstruction of the setting and showing the (inevitable) red tape and bureaucracy that limits and creates problems for the heroes.
SuperHero Alias: The Baron.
Powers: Teleport objects and entities through shadows.