Or, would you rather play Human warlord or Lord of Raldwik, Hero of the Three Rivers Battle?
I dare to claim that classes are bad for a roleplaying game. While I like character classes in a way, I've often found them a bit too defining. They are fine for straightforward dungeon delving or other similar games, but they take away from roleplaying, causing the class to be the role instead of the character itself. Think about a moment you tell your friend that you're doing a fighter for the upcoming d&d campaign. You can see his expression when he searches his mind for the player's handbook ironic fighter picture. If you tell him he's an elf, he updates his vision into the PHB elf picture.
While the character might be very different from the picture, and even it could be played differently, the mental picture once created can be difficult to change. I've even heard a few times 'What, is your character female?' for which I blame describing the character by it's class - well, in addition to player inattentiveness.
Even if you describe your character as a person, after a short silence there's someone who asks 'So, what is he?' Or, when someone tells that his character is merchant, others say 'Oh, rogue'. This and 'xp for kills and magic items from looting' -mentality might drive even a character who's player wants to play that bitter mercenary into just 'fighter'. The role is remembered now and then, but the character becomes primarily a fighter.
I'm curious about DnD Next. If my guesses about DnD Next character building method is right, it steps a step away from these forced archetypes, but still gives you a chance to play 'Fighter' if you want so. But if the character is primarily the person and only after it something more definable, it helps immersion in the game.
When it comes to D&D, I don't think WotC is ready to say goodbye to term 'Class', even if it would harm the game. Other game producers aren't tied up by traditions, and can use Professions, Talents or other terms instead. This is very close to Savage Worlds approach where players can buy powerful Professional edges, which usually have high specialized requirements.
How big problem do you think classes being primary definitive factor of a character is for a roleplaying game? How much does this affect your group? Do you think classes encourage games that are more focused on tactical combat rather than roleplaying?