Zigzagged in Groundhog Day, in which Bill Murray's character repeats the same day over and over again, with no way to stop the cycle. At first he's confused, and then overjoyed, but soon he's depressed as anything because he has no life to look forward to. However, eventually he realizes that the unlimited time can be used to master any skill, prevent any and all mishaps that would otherwise occur during his single day, and, once he learns to truly care for her, win the heart of his love interest. Which, it turns out, breaks the spell and canonizes that last perfect day as the one that actually happened.
In the Drew Barrymore film (and the later TV miniseries sequel) Firestarter, Charlie McGee inherits psychic powers from her parents who took part in a government experiment (They got lucky, most of the other patients went batshit insane). Her father got the ability to read minds and psychically "push" people to do what he wants or see what he sees, but it gives him pinprick brain hemorrhages to do so. Charlie doesn't have this problem, but her pyrokinesis (the ability to make fires by frowning) prohibits her from being close to anyone, due to control issues. To top it all off, the government agency that sponsored the experiment want to use her as a weapon. According to the film, by the time Charlie hits puberty she'll be powerful enough to crack the world in half. If that ain't this trope, nothing is.
In X: The Man with the X-Ray Eyes, the main character grants himself x-ray vision. While he obtains some benefits from it - including the ability to cheat at cards - his vision gradually increases in power until he can see through his own eyelids, through reality itself and into the swirling madness beyond. The deleted ending makes it worse. After ripping out his own eyes, he screams, "I can still see!"
In The Butterfly Effect the protagonist gains the power to go back in time and change key events in his childhood. But whatever he tries to fix he just ends up messing up his life and that of his friends even more. The Psychic Nosebleeds that follow shortly after changing the event aren't that nice either.
A major element of Matt Damon's character in Hereafter. He can read people's minds and/or communicate with their dead relatives by touching their hands. Cool, right? No. Imagine accidentally discovering the girl who you've been flirting with was sexually abused as a child by her father. Takes A Mind Is a Terrible Thing to Read to whole new levels.
In Ringu, Sadako Yamamura was born with extraordinary psychic abilities, which gave her clairvoyance, psychography, and astral projection that enabled her personality to endure after death and in the books, her abilities are powerful enough to allow her genetic manipulation of people and viruses. Her mother was also shown having similar abilities. Instead of fame and recognition, these powers led to both of them being scorned, driven away and persecuted by society, leading to Sadako's mother throwing herself into a volcano, and Sadako herself being killed and thrown down a well, where her spirit will linger forever.
The Ring: Samara Morgan had the innate ability to imprint images and visions in the minds of other living things; unfortunately, the power manifested at birth, and she was never able to control it, leading both her mother and adoptive mother into complete madness. The second film says that Samara's powers came about because her mother let dead spirits possess her, and while these gave Samara awesome powers, her body was pretty much hijacked and all she could do was watch as the spirits controlled her body and — often — caused problems for people. She spent her whole life asking for people to drown her, because that was the only way to get the spirits out of her body.
Godzilla. It's his own radiation that ends up being the cause of his own death in Godzilla vs. Destoroyah. Yes, we're talking about the SAME radiation that allows him to spew nuclear plasma and destroy his enemies.
It's no fun being a Scanner, mostly because of all that Power Incontinence. Also, hearing the thoughts of everyone around you gets noisy and distracting.
While Darkman is impervious to pain, he had to burn nearly to death to get that way, and to undergo a dubious surgical technique which left him subject to uncontrolled rage and mood swings. Plus, with no sense of pain, he can't even tell if he's injuring himself until he actually looks.
In the movie Death Becomes Her, two of the main characters take a potion that grants eternal life and youth. No, the suck doesn't involve Who Wants to Live Forever?, as most of the qualities of that trope are either ignored or handwaved (anyone who takes the potion is supposed to sever all human contact after so many years anyway, so as to avoid suspicion). The suck comes after both newly immortal characters try to kill each other, and find out that, while they won't die, their bodies will. From then on, they are stuck in their own broken corpses, having to utilize undertaking techniques just to keep themselves looking and moving like living people. By the end of the movie, even this isn't enough, as their bodies fall apart around them, leaving them spending what may very well be eternity as a pile of rotting body parts.
Being sensitive to the Force in Star Wars isn't really fun at all. Yeah it comes with nifty psychic powers and super reflexes, but Force Users have to maintain strict control over their emotions, sometimes to the point of being The Stoic. Otherwise they run the risk of falling to the Dark Side of the Force, and while this also comes with nifty (and scary) powers, spending too much time on the Dark Side inevitably leads to the loss of friends and loved ones, insanity, and death.
After slipping into a deep depression, the younger Charles views his telepathy as a curse because he can no longer control it. He is unable to shut out the clamour of thoughts that he doesn't want to hear, and this causes a tremendous amount of agony, to the point where he becomes addicted to a serum which numbs his ability, allowing him to sleep at night.
At the age of nine, Xavier believed that he was mentally ill (schizophrenia, most likely) due to the voices in his head, and it took him three whole years to recognize that he was actually telepathic—as dysfunctional as he is in 1973, his childhood experience must have been downright nightmarish in comparison.
Those who take the Mark of the Beast in the Apocalypse film series are blessed with limited telekinetic and telepathic powers and can also receive miraculous healings, all at the cost of spending eternity in the Lake of Fire.
The protagonists from the Final Destination series (Alex Browning, Kimberly Corman, Wendy Christensen, Nick O'Bannon and Sam Lawton). The visions in regards to the impending disasters along with their own demise drives the plot of cheating Death. Either that, or Death is pretty sadistic or he is a sore loser.
Men In Black III introduces Griffin, an alien who can see all possible timelines at once. When he shows J and K the Mets winning the 1969 World Series three months before it'll happen, J says it's incredible; Griffin calls it a pain in the ass. Unusually for this trope, though, he does seem to enjoy the ability to some extent; he refers to said World Series as his favorite moment of all time, because of all the insanely improbable things that came together to make it happen. Though at the end of the film, it's replaced by the moment where J gets back from the past and meets up with K, who's (slightly) less Stoic thanks to the events of the movie.
In Man of Steel, when young Clark's X-ray vision and super-hearing first manifest, he freaks out from sensory overload and locks himself in a closet.
All of the Precogs of Minority Report are cursed to foresee events that have yet to come, Agatha especially. Throughout the movie, she tells random people and Anderton things she's seen happen. She even sees her mother's death replay in her mind.
Elsa in Frozen considers her powers this until she learns to control them. Having strong powers over ice and snow is cool. Nearly killing your little sister when you are both just children and years later accidentally putting your whole kingdom in eternal winter due to Power Incontinence is not.