If you think that font names in CSS require quotes around them when they contain spaces, and don't require quotes when they don't, here's proof that that's not always true.
Example 1: "Times New Roman" with and without quotes. As you can see, these styles are treated exactly the same, even thouh the font name does have spaces. There's no difference.
Example 2: And here are some font names in one word, that shouldn't require quotes, but actually do, at least in Internet Explorer. Suppose you have a font named "Caption", then in the first line, the whole font style is ignored, because Caption without quotes is a keyword, and IE does not treat it like a font name.
Example 3: Same here, with the names "Default", "Initial" and "Inherit". Again, those words without quotes are keywords. And this example affects most browsers, not just IE. Note that if you don't have fonts with those names, you can still see that it is problematic, because the font size doesn't increase.
Example 4: And the last one, for some font names that are not keywords, but do contain non-letter characters. These also require quotes or they won't work.
Conclusion: unless your font name is one word and you're really sure that the font name is not a CSS keyword, in current and future versions of CSS, better be safe than sorry and always put quotes around your font names.
Bonus example: Some untried font names.