What happens to my 401(k) if my company goes under or folds?

Your 401K goes through an independent company, so it should be fine if the YOUR company collapses, although the method of introducing money into this account will change. You might have to pay fees or not get the same rate of return when the company collapses, but you don't have to worry about it disappearing (unless you work for a financial firm, of course).

However, if all your money is in a traditional pension, then you have some worrying to do. No matter how stable a company is, always make sure you don't solely depend on a pension for your twilight years, because pensions sometimes collapse with the company.