Butter, indeed, goes bad—eventually. Much like hot sauce, ketchup and other pantry essentials, it’ll last at room temperature longer than you think: ten to 14 days, actually.
Why? Butter’s high fat content makes it less susceptible to bacteria, which keeps it from spoiling right away (and is why most parts of the world keep their butter out). But because dairy in the U.S. is pasteurized, there's a misconception that butter needs to be refrigerated. Long story short, the U.S. uses high-temperature short-time pasteurization (HTST) on milk, which kills bacteria in big batches. It's cost-efficient for manufacturers, but also makes refrigeration necessary. But because of butter's comparatively high fat content, it doesn’t actually need to be stored as strictly as milk.
Of course, if your butter has a sour smell or taste, mold or discoloration, play it safe and toss it away. Until then, it’s probably good to eat.