From the global perspective, cheap oil is a very good thing. Cheap commodities in general are an unmitigated good thing. Cheap oil means that people spend less money to move vehicles around and heat homes, and can spend it elsewhere. Cheap oil means trade is cheaper, allowing goods to be produced in more-efficient places and then shipped instead. Cheap commodities mean that investors spend less money building oil rigs and mines, and can invest it elsewhere. Final goods and services where oil or other commodities are an input become less expensive, allowing other economic activity to be pursued.
The reasons cheap oil could be linked to bad stuff in the world economy are not because the oil itself is cheap, though. Cheap oil could be bad because it is a sign that no one wants to buy oil, which is a sign that people aren't shipping goods and other economic activity is depressed. (This is a cause of cheap oil, though, not an effect.) The other big reason it could be bad is that it is a sign that people have invested too much money drilling for oil and building oil-extracting machines and training people to be oilfield workers and the like. Too-cheap oil suggests that this investment was a bad idea and should not have been made, or at least not made yet, and now that effort has been at least partially wasted. But that's another cause of cheap oil, and not an effect.
The people who suffer from cheap oil are those who are involved in the production of oil: oil companies themselves, companies who provide services to oil companies, pipeline companies, railroad companies involved in shipping oil, workers out on the oil fields, companies involved in providing services in those regions (e.g. real estate firms in the right parts of the Dakotas)... and investors in any of those companies (including pension funds).
The US is involved in a lot more oil production than it used to be, so some of that suffering partially mitigates against the awesomeness of cheap oil to the rest of its economy. (Partially. Most of the US is not involved in producing oil.)