1. They add variety and replay value, no matter what game style you are using them for.
2. Depends on the context in which the class system is used. In general if it's an rpg, I perfer flexibility, but if it's some other genre of game that borrows rpg elements (or isn't an rpg but still has a class system), then having the player stay with his initial class seems  like a more intuitive decision to make. (it's also a good way to make replay value a plus)
3. If you are going through the trouble to build this style of functionality in your game, I can't help but expect there to be a good reason for you doing so. That being said, it's impact in your game if you choose to design one for it should be in direct reference to the reason you decided to make a class system for that game in the first place. Like the previous question, it's all a matter of context. If you know you need it for your game to work, then the player should understand that as he is getting to know the class system for himself.
4. Context. How the hell am I supposed to know how classes should be limited if I don't even know what the classes are yet? I mean, shouldn't it be based on what the classes are to begin with? If you are going to give a wizard a broadsword, then you either need a class system that takes the idea of a class with both capabilities into account, or simply have your game in a setting where it is apparent wizards commonly use broadswords, so that the skill isn't awkwardly or arbitrarily placed within that class.
5. You should reward the player for locking himself in when he initially chooses the class. You also need to reward the player as he accomplishes the things in your game that count towards progress. These are the important things you need to consider, and any specification beyond that is just in the technical implementation based on the type of game you want to make. I've said it before, and I'll say it again: context!
Extra layers of customization work especially well with a points system for instance, but so does complexity. Players can play your game much more easily if they don't have lots of extra stuff they need to manage before advancing, so you have to make sure whatever you ask of the player outside of the play itself is going to be worth it during those moment of actual play. No matter how robust it makes your game, extra menus and options are always going to be an obstacle the player has to get through in order to get to the play itself.

1. Do people even give a hoot about Class systems anymore or are you discouraged by them?

Yes we do as long as they are implemented properly.

2. If a game did have one would you prefer to be able to change classes at will or a "One choice and you’re stuck with it" system?

I prefer to change at will, since it will go into what I will explain in the next sentence.

3. Exactly how should the Class system impact the game in your view, for example, like FFV where the story seems to revolve around it or more like an extra add-on?

Either it doesn't matter to me.

4. Do you prefer classes to be restricted to what kinds of equipment they can use or do you prefer more freedom in that department?

The more flexibility the better, why? Because it lets the player customize, knights can use bows, spears, swords and axes, same with samurai's and ninjas. Maybe you should  take a look at FF5 where you can make a character learn a skill which will let them equip axes, swords and other weapons etc.

5. Should Class skills be learnt as you level up or acquired though other means? (Such as buying them with Points or the like)

Classes I think should be learnt or should be obtained by using required points to obtain them.

Try to be flexible with this, imagine letting the player make a mage that can use swords, making a knight learn basic black magic and etc. There are many possibilities and this will give your game more replay value as players will take their time to customize each and every one of their characters for a specific job or duty.

I am assuming you are talking computer/console RPGs here.
Do people even give a hoot about Class systems anymore or are you discouraged by them?
The kind of variance provided by a class system tends to make RPGs more fun. The kind of variance provided by a skill system that implies a class system without outwardly constructing and naming one is cooler, but also somewhat harder to balance/design. I prefer the latter in games where character development is in the hands of the player(s). Omitting a class choice system, however may allow you to tell your players more about the characters in a more story based game by how they and their stats (or equivalent) develop. Adding replayability in such games is still possible by allowing characters an individual skill tree or similar 'progression system'.
If a game did have one would you prefer to be able to change classes at will or a "One choice and you’re stuck with it" system?
If I chose my class initially I like being able to choose again. Perhaps as I advance, the different classes available to me will change, however?
Exactly how should the Class system impact the game in your view, for example, like FFV where the story seems to revolve around it or more like an extra add-on?
If you are developing a story based game then you should probably have a sensible reason that your characters have 'classes', yes. I'm of the opinion that any game mechanic that is just tacked on as an extra feature should be removed. A game is not a feature list.
Do you prefer classes to be restricted to what kinds of equipment they can use or do you prefer more freedom in that department?
Depends on the game's setting and what role the class system serves in it. Also depends on how you want your battles to feel. This is a 'think carefully and then playtest' decision.
Should Class skills be learnt as you level up or acquired though other means? (Such as buying them with Points or the like)
Skills should be obtained in a way that meshes with the overall feeling you're going for.

Thank you for the tutorial on game planning Rajew. Now I will know to plan all of my games as lists of features and nothing beyond that. Actually I think that the same principle could have a valuable *cross-application* into the field of novel writing:

my book
features:
- words
- cool car chase
- picasso shows up
- gold plated cover
- gold plated pages
- sits on a plate made of gold

This is the way to proceed. Now to fetch some words...

Really biggles? You quoted Rajew as saying that the only thing a game is in the planning/paperwork stage is a feature list?

Because I'm looking at what he said right now and I don't see him explicitly stating that anywhere. He said that a game is a feature list in that stage, but you jump to that conclusion based on the assumption that it is impossible for it to be more than one thing at the same time.

Maybe you are just mad because when you heard the words "the most important phase of development", you expected a comprehensive tutorial on initial game planning and documentation, but all you got was a reply to the actual topic of discussion.

I could make that tutorial myself, but if what you say about it's cross-application with writing is true, you would be just as happy with me only posting the feature list of such a tutorial:
my comprehensive game planning tutorial
features:
- lots of words
- strategies for finding the comprehensive goal behind your game's design
- quotes from famous people of the game development industry
- advice on how to outline and document your ideas in an easy to understand matter
- making your feature list (obviously the most important part)
- encouragement

EDC, you can read my post as "fuck you, that's not what I meant at all. i know what game planning is." if you like. The entire text he was responding to was:

If you are developing a story based game then you should probably have a sensible reason that your characters have 'classes', yes. I'm of the opinion that any game mechanic that is just tacked on as an extra feature should be removed. A game is not a feature list.

And by 'a game is not a feature list', I meant that just writing down a list of "cool features" with no relevance to one another is a thoroughly incompetent way to plan a game.  I responded with the assumption that rajew had understood what I meant and disagreed.

I don't think that the entire game industry follows an identical approach to game planning, somehow. I don't think that the industry necessarily plans games perfectly every time either. Personally, I see games as a way of expressing to other people what you think is fun. I'd start planning a game from some overall idea or theme or message (or several) and then fill in the details in terms of how various game mechanics fit together to achieve it. Lists could still be used in writing this down, yes, but the overall feeling shouldn't be just a "list of cool stuff to put in game" but rather a system of rules that fits together to form something more cohesive (and maybe meaningful?).

oh no! not epic fail! if only the mighty wisdom of the commercial game producers was on my side... then i could survive in this harsh and confusing environment of video games development.