Honestly I can't think of the last time I ever actually used a 'forward' button on either a web browser, or in Windows. We all use the back button, but most users I observe including myself, simply click an item rather than using the forward button.
So the simple question stands, is a forward button actually a necessity to any application, - at all - ? If so, why?
It's not useful to the application; it's useful to the user.
I use it all the time, (well, not all the time). It comes in handy just after you click 'back', but then decide you want to go back to where you were, and wish to avoid reloading the page :)
I tend to use it once in awhile. Very often (especially when doing research for school), I will read something, then realize I read something relevant a few pages back, and I'll go back to that page. Then, I open it in a new tab, and go forward to the latest page I was on again.
I can't say that I use it often or that I see a lot of people using it, but it definitely has its uses.
Especially in scenarios where someone hits the back button more times then they wanted. (If they didn't know how far back they wanted to go, or are just plain impatient), it becomes a necessity.
It's easier for users to seek to a static, well-known area of the screen to go forward, rather than search the document for whatever they had previously clicked. In the case of large/complex documents, the difference may be significant to the user. It's even easier to use the forward hot-key.
While not absolutely necessary it's helpful to have in the application because users respond well to mechanisms that are fast and easy.
As with any feature in a piece of software, it's "needed" if the people who decide on the features list (be they developers or salespeople, or others) determine that users might find it useful.
That determination may be based on user feedback, testing, experience or guesswork, and it's very hard (if not impossible) to get it right for everyone!
To address the feature specified in the above question, yes, I use the "Forward" button in both the web browser and Windows Explorer. In addition, I find it useful enough to have it mapped to the thumb button on my mouse ("Back" is mapped to the scroll wheel button).