I'd hate to think this rising feeling of panic wasn't thoroughly justified.
Noblesse: Raizel never does any hand-to-hand combat. His job is to come at the very last minute and put the finishing move on the enemy. Problem is, every time he uses his power, it eats away at his lifespan.
In Haru-Sari, elves can use magic better than humans, but are considerably less sane and die when they're about 30.
Black Mage from 8-Bit Theater gains the ability to learn any spell used against him. However, all the spells he learns with it were cast by Sarda, and therefore were invented on the spot specifically to harm Black Mage. For example, Sarda casts a spell targeting Black Mage that makes BM puke his intestines out. Black Mage then uses that spell while targeting Sarda, which thus causes BM to puke out his own intestines.
When it manifests on a rooftop and drags Antimony (and, they later learn, one of the boys they're with) along for the ride, Antimony suggests the possibility of learning to control it... at which point Zimmy explodes at her. Later, though, Zimmy reassures Annie that "it's only as real as you let it be"-implying that, for once, denial is an effective coping mechanism.
And Gamma's ability to nullify Zimmy's power is no better. It doesn't work as well when she's asleep, but she can't bear to make Zimmy suffer, so she tries to stay awake as long as possible and that takes its toll on her.
Coyote gave Reynardine the ability to possess others' bodies, then return to his own. Coyote himself could use this ability harmlessly, but for reasons that Coyote implies he doesn't know, Reynardine invariably and unintentionally kills his host upon leaving their body.
Coyote gave Ysengrin powerful arms made of wood, and with them, the power to manipulate trees. The downside is that they're apparently arthritic. Coyote freely admits that he screwed up, but Ysengrin insists that he has no complaints. (Ysengrin is fanatically devoted to Coyote, so it's possible that he does have complaints, but he either keeps them to himself or is in denial of them.)
Andrew "Smitty" Smith has the power to subconsciously create order in chaotic situations; he can, for example, throw a deck of shuffled cards in the air and have them all land in a neat sorted pile. The first major display of his power, however, comes in chapter 23... where he manages, in the space of about an hour, to ruin a VR simulation game that his friends were looking forward to by causing the objective treasure to spawn at his feet, and then causes the girl he likes (who has teleportation powers of which she is unaware and who also likes him) to subconsciously teleport the two of them onto her bed, along with the teacher and two friends they were with at the time.Hilarity Ensues. Later issues suggest there is a downside in misfortune befalling others to bring about fortunate events for himself. This is first demonstrated by the girls bringing him in to get a blinker stone close to the shore, which succeeds because his throw strikes a passing bird. He later describes how he could potentially use his powers to cause events that would lead to his girlfriend teleporting to him, but these events could be wholly negative such as her seeking help to assist her mentor who suffered an accident.
Fire elemental ancestry. The good thing: a lot of magical power, transferring down the generations fully — no dilution or genetic lottery. Packaged with very lively spirit and general attractiveness. The bad thing: the life starts with witnessing your predecessor waste and die just when things start to get really interesting, and ends early, in exactly the same fashion. No variants. If there are ways to cheat the system without making things even worse, several generations of experts in magic and Etheric Sciences failed to find any, despite access to vast variety of very cooperative magic creatures up to and including at least one Physical God.
Sir Thane from Bloomin' Faeries was blessed/cursed by the faerie queen to be irresistible to any woman he comes across, eternally erect and to spout non stop foul language during sex. He considers it a curse since he causes 'every' woman he meets to uncontrollably want to have constant sex with him regardless of how old, married or giant Orcish they are. However, he has used this to his advantage since a side effect of the curse also causes any woman who sleeps with him to become busty, beautiful and amorous no matter how they looked before. Even the old hideous Orc he was with turned into a beautiful object of desire.
The titular character of Dominic Deegan started out as a mere seer, but as the story got deeper and darker, his powers seem to have made him Blessed with Suck. He keeps constantly getting into conflicts that he wanted nothing to do with, all because he's the only one with the visions that can save everyone. This recently led to a nervous breakdown, proving his powers now seem to be more of a curse than a blessing.
An even better example would be the Resistants. A Resistant is a person who is born with complete immunity to any and all magics. This initially sounds like an incredible blessing (given how most of the Dominic Deegan world revolves around magic), but remember that this means that healing magic is just as useless to a Resistant as offensive magic, meaning that if they're seriously injured, the normally live-saving White Magic won't help them at all. In addition, most people who use magic to attack will find a way to attack a Resistant indirectly, such as in the Snowsong arc, where the titular villain, upon finding that her ice magic wouldn't work against Dex Garrit, simply froze the ground he was standing on, causing him to slip and reducing his usefulness. Failing that, a magic user can just hit a resistant with something very very sharp...
Quentyn, the main character from Tales of the Questor, is (while drunk) accidentally "bonded" to a magic sword. While this normally conveys some few advantages (no one but he can use the sword, he can normally locate it wherever it is by "feel" and, under the right circumstances, summon it to himself), it is outweighed by the considerable number of drawbacks: first, it is implied that in the wrong hands the sword could become a magical conduit back to himself, second, no one else can use the sword 'even if he wants them to;' third, separation from the sword beyond a certain distance causes him chronic and growing discomfort and anxiety; and as a final kicker, the sword itself, while being quite magically potent, is something of a flawed design — its magical effects, when drawn, are 'entirely random....' varying from incredibly deadly to wildly uncontrolled to comically useless.
Possible example from the Order of the Stick prequel book, Start of Darkness.Xykon was... slightly less Ax-Crazy as a human, before discovering that becoming a lich cost him his sense of taste. Apparently, killing minions is the only pleasure that compares to a good (or really bad) cup of coffee.
Another example: when the party drew straws for choosing magical items, Roy went last and got the Bag of Tricks. It holds balls of fuzz that, when thrown, turn into any of a number of small animals "as long as they are completely useless in battle." One exception is when his target deflects the ball of fuzz into the air. Naturally, it turns into a rhinoceros and lands on Roy.
Earlier in that quest, however, he does find a couple of uses for the bag. One is to make the team's cantankerous loudmouth shut up by flinging a badger into his face. Another is to sneak up on sentries one by one, then summon a kitten to distract the sentry long enough for Roy to knock him out.
One of Aylee's many forms in Sluggy Freelance had the ability to give off an electromagnetic pulse, disabling any electronic device in the area. However, she couldn't stop herself from give off these EMP burst, and when one of them erased Bun-Bun'sBaywatch tapes, it almost got the entire cast killed.
Oasis may be the more prominent example of this trope. Immortal (comes back to life quickly after dying, but ages and takes damage normally, though any injuries are repaired upon revival), pyrokinetic (Hulk-variety Power Incontinence on that one), and a trained killing machine, but due to an evil mastermind's plot, she is forced to obey any command he speaks into his wristwatch. Said mastermind dies, but any standing orders remain functional, including a compulsion to brutally murder anyone with even the slightest association with Hereti-Corp (she slaughters patrons of a chain of pizza restaurants that uses their logo) and a compulsion to harbor an undying love for the comic's main character, going as far to hunt down his love interest. All of this turns her into a Death Seeker, and in the midst of this she realizes that she is, in fact, immortal and will come back no matter how many times she dies.
How about the AWESOME power that Zoe gains when Torg gives her a magical necklace? The true power of suck just radiates out of that thing whenever the magic words are spoken by anyone who knows them and turns her into a camel. She does finally get rid of it but at a horrific cost.
Tower of God - 25th Baam's incredible talent with handling Shinsoo and his lack of contractual fetters due to his status as an Irregular make him one of the potentially most powerful characters of the story, but exactly these qualities attract people who want to use him. And they succeed by breaking his spirit and threatening to kill his friends.
Elliot and Ellen of El Goonish Shive are developing magic powers. The downside is pretty severe Power Incontinence, which is especially bad for Elliot, as he has to transform into a girl multiple times per day - a prospect he is not happy about. Said Power Incontinence will eventually wear off, and there have been debates as to how bad they have it anyway, but Word of God states that the suck outweighs the blessing for now.
And Elliot's transformations have an effect on his personality as well; he develops a superhero form, which is awesome, except the whole "turning into a girl" part. Comes with a few alter-ego forms. One is a "party form" that works well as a disguise, but causes him to kiss his girlfriend's sister on live TV. This can be averted by Elliot not transforming into that particular form, but it's implied that he actually enjoyed it (apart from the kissing thing). Another has existential angst built in. The third is emotionally and mentally awkward and prone to feeling embarrassed or otherwise inconvenienced and needs glasses.
Tedd later gets the ability to switch genders anytime he wants... even though he already has multiple easy ways of doing so.
Darren Danforth of Penny and Aggie makes every girl (or at least every heterosexual girl) see in him her dream of the ideal lover. Since he's really a dim good-natured klutz this sets them both up for disappointment.
In Homestuck, Jack Noir. When Bequerel, Jade's omnipotent dog, prototypes himself to save her, this inadvertently causes the creation of Bec Noir. He's inherited all the traits of Bec now. All of them. That includes teleportation, near-invulnerability, extra-sensitive sense of smell... and the inability to kill Jade out of forced love and loyalty.
Becoming one of the most powerful forces in the series also brings with it extreme boredom when you don't have an end goal beyond "kill things." And even then, you have to be careful not to destroy everything because then there'd be nothing left to destroy.
The classes Mage and Seer are more or less built around this. They have an advanced comprehension of Sburb and their Aspect and can use this in battle, though so far they have all been hurt or damaged by their Aspect in some way, at least until they embrace it and have some Character Development, which is par for the course in Sburb.
Rose, as the Seer of Light, is able to predict the future using informed and uninformed decisions, as Light translated roughly to "Fortune" or "Knowledge", meaning that she is effectively "someone who benefits others with fortune". To put it lightly, good things do not happentoher. Also notable is that her Grimdark state was caused by asking her crystal ball for an answer - Light representing truth and honesty - and being given the answer, said honesty causing her to go insane.
Sollux is the most obvious example, being the Mage of Doom. "Doom" is often associated with figurative structures and, of course, death, as is Light. He has died many, many times, though has always ultimately survived via some convoluted or obscure measure.
Terezi is the Seer of Mind, and is thus able to see all consequences of all actions that are made around her. When she sees that Vriska's leaving to fight Bec Noir would lead him right to her and Karkat, and would thus get them killed, she eliminates the possibility of this timeline by killing Vriska, causing her to die a Karmic Death and not be revived. This creates a better timeline, but still a doomed one that John eventually saves with Terezi's help, making this both a deconstruction and a reconstruction. It also doesn't help that she was blinded by Vriska, mind controlling someone, who then mind controls Terezi's lusus which is then mind controlling her into staring into the Alternian sun.
Meulin is the Mage of Heart, and so far has been shown to be an excellent matchmaker, despite her own love life being very bleak and unsuccessful.
Sore Thumbs recently went through a Continuity Reboot after Jimmy Peterford fixed the world. So far, most of the characters that have been reintroduced since then have had their problems fixed in a decidedly "Blessed With Suck" manner. Cecania is finally a horror show host... but it's on the notoriously stupid G4TV, and they cancelled her show for no immediately obvious reason just as the comic restarts. Harmony is once again an immensely talented brain surgeon and now has the respect and admiration of her peers... which would be good, except she hates being a doctor. Sawyer is now recognized as a war hero, and his mother is alive and he still has his penis... but his mother turns out to be a shrill, nagging, controlling shrew, and without losing his penis, he doesn't even have the terrible "video game distributor" job he had at the start of the original run — judging by what we've seen, he's spent his days laying around being nagged to get a job and having any potential girlfriends scared off by Coleman or his mother. It's still better than the alternative (being dead), but...
Tainting also counts. By infusing their aura/souls with "demons", Drow are inoculated against forceful Demonic Possession and, depending on the strength of the spirits, gain a significant power boost. Diva'ratrika's daughterscurb stomped their own mother thanks to said power boost. Attaching an Eldritch Abomination to your own soul isn't free of risk. Going From Bad to Worse, according to Sha'sana, the one who came up with the practice of Tainting in the first place, Snadhya'rune's brand of Tainting which apparently uses more powerful demons is dangerously unstable and her Tainted Drow will have at most fifty years before their demons overwhelm them.
Ménage à 3 appears to be fairly realistic, as webcomics go, with no superpowers. However, it features at least two instances of this trope:
DiDi, an Amazonian Statuesque Stunner, can attract men (and not a few women) without even trying, and seems to quite enjoy male company and sex, in principle. Unfortunately, her beauty seems to have scrambled her ability to develop ordinary social skills. Moreover, her sheer attractiveness induces premature ejaculation in men, she has trouble reaching orgasm anyway, and her social and emotional incompetence stops her from communicating with her lovers properly. As the comic progresses, orgasm deprivation drives her downright crazy.
Slightly more subtly, Gary, who starts the comic's run as a desperate virgin, somehow gains the ability to attract large numbers of attractive women through a peculiar combination of adorkable charm, niceness, and legendary oral sex technique. The women include a psychotic phallophobe, a narcissistictranssexual lingerie model, a ruthless dominatrix, and the deranged DiDi. It's a shame that Gary never acquired any kind of assertiveness or judgement.
A teenager wished to be able to see through clothes. All cloth became invisible to him so now he has no way of knowing if he is dressed or not. Any attempts to wish this away are implied to only make things worse.
A guy wished for what is presumed to be amazing sexual prowess. Now any person who attempts to stimulate his penis in any way instantly gets a mindblowing orgasm and falls asleep, including his own hand. Naturally, he alternates between sexual frustration and blue balls.
Backfired in the case of a guy who defiled a tomb and was cursed to be the best in the world at blowjobs. The intent was that he either hide his talent forever or be forever known as the blowjob guy. He uses his talent to become king.
Union of Heroes: Lynn's super-power is to die in the place of other people (and then to come back to life herself). Sure, useful for rescuing people in lethal situations - but dying over and over again, and often quite violently, certainly hurts...
Val of Sidekick Girl is a Type VI Immortal - she can't be killed, but she doesn't heal any faster or resist injury any better than normal people. As a sidekick to none-too-bright superheroine, such grievous bodily harm is frequently part of the job.
Yrek's situation in Interstellar Tea House looks to be this. He's some kind of constructed shapeshifter that can take the forms of two (or more?) different sentient species. But he's being hunted, probably as a result, and once you're a homeless fugitive being a homeless fugitive that isn't quite the same species as anyone else doesn't help things.
Abductees in the Walkyverse. Each of them was kidnapped by aliens as a child and had martian DNA grafted onto their own. This gives a variety of superpowers, most commonly super strength and endurance, but occasionally something more exotic like super speed or spinning like the Tasmanian Devil. The downsides are that A) You are susceptible to alien Mind Control, and they plan to use you as an army to take over the world, B) you were abducted multiple times during your life so the aliens could check on your progress, had your memories erased, and now contain a subconscious trigger that makes watching The Sound of Music excruciatingly painful, and C) as soon as the secret government agency SEMME finds out about you, they will force you into their ranks to hunt aliens whether you like it or not.
In Wapsi Square, Justin has the power of regeneration. Unfortunately, he has none of the Badassery that usually accompanies this power, and he is a magnet for supernatural women. Because of this, several of his exes did some rather nasty things to him on the grounds that "You'll recover in a minute anyway."
Parodied in xkcd: The magic shoes enable the wearer to outrun death itself and make them immortal... but they have those creepy individual toes.
Chuy from Girly is blessed with overwhelming sex appeal, to the point that women in the immediate vicinity can't help but throw themselves at him. This isn't a big deal in the beginning when he's simply a Kavorka Man, but after some Character Development, when he starts wanting a real, meaningful relationship, it becomes a huge problem.
The two unfortunate people from the "Common Men" chapter of Accidentals both have the power to turn people to stone by looking at them, which is probably the origin of the Medusa myth.
Herz from Friends Till Deathdefinitely qualifies for this. He has amazing fighting abilities and immortality, but his immense powers can make him horribly sick, he's an Eldritch Abomination disguised as a human, his powers and strange appearance alienate him from his classmates, and he is severely depressed and suicidal due to this.
Father Time from Night Terror suffers from a pretty extreme version of this trope. He can see alternate timelines... but he can't stop seeing alternate timelines. And since Night Terror is set in what could, at best, be called a Crapsaccharine World, he's forced to see his friends and family die in increasingly painful ways on a daily basis. To the point where he gouged out his own eyes just to make it stop. And even that didn't work.
Darren also suffers from this. He was created to attack and eat the shadow people that torment people with schizophrenia and sleep paralysis. He later developed an addiction to eating them, but if he eats too many, he risks turning back into his original form, Proditophobia.
Austen, the deuteragonist of Always Human, has a highly sensitive immune system. Ordinarily, this wouldn't be a serious problem, but the comic is set in a future where bio-compatible nanotechnology is practically everywhere, and she can't make use of it.