If you hire enough people, eventually you'll have a bunch of examples for this question, unless of course you never make mistakes.
Pretty much everything you can imagine can go wrong and probably more. Hiring anyone is always a risk but it's one you can't avoid, nor do I think that the interview process should be so tough as to have lots of false negatives to prevent those bad hires; better IMO to have a reasonable filtering process and then be on the alert for problems post-hire so they can be addressed early, including the possibility of termination.
That said, specific bad hire examples that were tough to deal with:
-Developers who get stuck and don't ask for help - spinning your wheels making no progress until someone notices is a great way to derail a project and make yourself look incompetent. Often times the things these developers get stuck on are quickly solved by some outside perspective, rubber ducking, or specialized knowledge.
-Negative attitude, high aptitude: a developer really good at their job but constantly sowing seeds of discontent, either getting into conflicts with others directly or subverting management directives, talking to others about how terrible the company is doing, etc. Letting an otherwise extremely competent person go is very tough so often they are allowed to remain way beyond when they should.
-Architecture astronauts/overcomplicators - maybe a cultural fit issue but some people are allergic to the move fast and break things approach, focusing way too much on nebulous code quality aspects, high levels of abstractions that often end up interacting in weird ways that are hard to debug, with the aim of high levels of code reuse and extensibility, but in the long run often leads to the need for major refactoring when underlying assumptions change. It's not that these qualities are are always bad and never work, but some developers are seemingly bored working on less complicated systems and majorly over engineer even things intended to be thrown away or overhauled later, so often times is a huge waste of time and ends up being more difficult to maintain. Of all the bad habits or deficiencies developers can have, this is the one that I haven't had much luck with intervention on.
-Lone wolf - some developers are great in one on one interviews and are quite capable, but turn out to not work well with others. They either refuse to follow processes, or on group projects will just do what they want even if it doesn't match what the group decided, they might decide that a midnight refactor of a core piece of code someone else is working on is something they have to do right now, and not even bother giving the other person a heads up. Sometimes you can give them sufficiently isolated projects that they can work effectively, but in the long run it doesn't really work, and you risk harming the rest of the team.
-Sloppy / lack attention to detail. Developers who fail to check their own work, or do it so hastily they don't notice glaring mistakes, or who are rushing so much they don't / can't follow a simple spec. These developers also often have trouble following coding standards because either they never learn them or they're not really looking at their code enough to notice when it doesn't follow.
-Not curious / quick to BS through a problem. Debugging skills are critical to being a good developer, but some developers don't spend much time or effort figuring out how to effectively debug their code and surrounding systems, so as soon as something goes wrong they have no idea where the problem is, are often quick to resort to ghost stories to explain the phenomenon, I.e. blaming a heisenbug that's caused by a race condition on the browser, a failed request caused by a network outage on the API, etc. These developers are frustrating to help because even when you teach them how to investigate these issues, their lack of interest means they'll never pick it up. Subsequently they're more likely to ship bugs because they're good at convincing themselves that bugs they observe are not the result of their changes.