I say that for anything but a trivial web application, you should version it. There are two, slightly different, notions at work here:
- application as a whole
- individual files
Regardless of the situation, I believe that files should have individual version (or revision) numbers. Ideally, this would be handled automagicaly by your version control system. As it has been stated by others, it's easier to refer to a file's version number than its date-and-time.
If you have (or may have) more than one live installation of the application, it should be versioned as a whole. This is also a good practice if you have separate dev and test environments (as you likely should). Each application (or release) version number refers to a collection of individual files at specific version numbers. While dealing with all of this is an extra burden, it is easier to check-out a specific release than individual files at specific revision numbers.
This makes me think of a notion in linguistics. It is said that if you can't express something in a language, you can't think about it (in that language). I think of the German word 'Schadenfreude.' It is much easier to think (and speak) of this notion of "feeling joy due to someone else's misfortune" by referring to that word, than its definition. That is the reason the word has crept into use in the English language.
Similarly, version numbers make it easier to speak (and think) of your application and its files at specific states. If you're a one person team, working on one application, it doesn't likely make a huge difference. However, as things get more complicated it is better for you to have these labels available for use.