So, I have this idea for a character.
He's fresh out of Hero School, having been schooled in the basics of dungeoneering, party dynamics, roles and tactics, and like that. He just... hasn't chosen a class.
I mean, well, mostly.
He'll start out as something reasonably solid -- Ranger, maybe. But for his next level he'll take something else: Sorcerer, perhaps. And then Druid. And then Rogue. And then Barbarian. And then Cleric. Bard. Wizard. Maybe grab the first level of a prestige class or two, if he meets the prerequisites and we're using the kind of system where that exists.
This is, to be clear, an absolutely horrible idea. In DnD 3.5... well, for one thing, in 3.5 my current DM would never allow it. He gets twitchy about us having more than three classes total. But mainly, what you'd end up with here was a character who was both tremendously versatile and (I think) suicidally underpowered... but also hilarious. I'm still relatively new to Fifth Edition, and the power scaling is very different there, but I think you'd still have basically the same problem, just not quite so much of it.
The thing with D'n'D is that as a general thing, you should pick a general role and stick with it. If you're going to cast spells, focus on casting spells. If you're going to hit things with a polearm, focus on hitting things with a polearm. If you're the one who makes friends with the townsfolk and talks your way past the guards, focus on those skills. It's not that an individual character can't be somewhat versatile, but if you try to do everything you're rapidly going to hit a point where you can't do any of it well enough to be of any use.
DnD generally expects you be versatile by working as part of a group.
And yet... I still love the idea of this hopelessly enthusiastic kid who just wants to try everything, and see everything, and get out there and Do All The Things. And I'd love to see if I could find a way to make him playable.