I was doing some research for this question, and that brought to my attention something that doesn't add up.
According to Half-Blood Prince, Hermione achieved eleven OWLs:
'Oh, come off it,' said Ron, striding over to her and whipping her results out of her hand. 'Yep - ten "Outstandings" and one "Exceeds Expectations" in Defence Against the Dark Arts.'
Half-Blood Prince Chapter 5: "An Excess of Phlegm"
According to Pottermore, there are twelve OWL subjects:
- History of Magic
- Defence Against the Dark Arts
- Muggle Studies
- Study of Ancient Runes
- Care of Magical Creatures
Of these, Hermione was taking ten in fifth year: she dramatically drops Divination about midway through Prisoner of Azkaban, and she says at the end of that book that she dropped Muggle Studies.
We can confirm this number, since Harry's OWL results (And complete class list) is printed earlier in the chapter: he's taking nine courses. We know Hermione is taking Ancient Runes and Arithmancy (She frets about how she screwed up the exams for those courses earlier still), and she's not taking Divination; otherwise, their classes are identical.
So how did she get eleven OWLs? I could accept that she'd be able to write the exam without taking the class (And pass with flying colours; it is Hermione, after all), and for Muggle Studies I'd take that as valid, but it seems like something she'd dismiss as being "Too easy" - the reason she dropped the course in the first place.
Honestly I suspect the answer comes down to "JKR sucks at math", but I was curious if this had ever been addressed in canon.