Balance is a bugaboo...a bugbear, as Stormonu said, though I mean it in the more "nasty imagined figment" sense. It is a construct which gamers have created for themselves and, as most such constructs, has no "real" definition or objective meaning.
Different games/systems have different parameters of what makes "balance". Different characters within a game may be "balanced" among each other, or simply an individual character may be "balanced" within themselves/against the game/system (able to handle any/all situations with a reasonable expectation of success).
There is no "true" meaning here. It is all the perception of the player as to what makes "balance" or "imbalance."
As several have stated here, AD&D is seen as "unbalanced" by today's constructed, loosely understood, standard. Yet, back in the day, the very idea of "balance" did not play into character construction or choice at all. You looked for a "party" to be complete, i.e. "balanced", having sufficient resources and characters of various expertise that meshed together to, hopefully, be able to handle whatever challenges were presented to them.
The idea that my character should be "just as good" as you character in all things, except I use magic and you use a sword (or mace or stealth), and if I'm not, the "the game is obviously unbalanced" is absolutely ludicrous to me. I can do things you can't and you can do things I can't. Working together, we can do just about anything. That's my understanding of balance.
You're great at high levels and I'm not. Wah wah. I call "IMBALANCE!" The game is "flawed" and "unfair". My character is being "penalized" cuz he can't shoot fire out of his hands and I can't. I can only hit pretty much anything that moves and do 200hp of damage in a single attack. Wah wah. (a bit of hyberbole, but just a bit, and I trust the point is clear)
(I won't even get into the fact that whenever I see the AD&D MU v. Fighter arguments as an example of "bad balance", all I think of is that at high levels, a fighter character was supposed to get/build/raise a castle and veritable armies of retainers and mercenaries at your command. While the high level wizard was basically still all by his lonesome...maybe with a few low level apprentices in tow. The fact that most fighter PCs that I've known didn't bother to do that is not the game's"being unbalanced" fault).
(speaking in D&D terms here, if that wasn't obvious) It's a Role-Playing Game! Not a board game. Not a video game. Not a miniatures war game. Nor is there any rason whatsoever that it should be trying to emulate any of those things. Do what you have to do, in game, to MAKE yourself great (or equally great to that guy, or "better" than that guy since that seems the major concern) if that's what you want.
There doesn't need to be any "game design mandate" that says your (PC) chances and abilities should be "as good as" everyone elses. No where should it say your character automatically gets (or has an "even chance" to everyone else) to succeed in all things or that there is some point at which you "win". You can win a board game. You can win a war game. You can win a video game. If you "need to win", you may be more gratified playing one of those. As stated above, RPGs are none of those things.
It's a playstyle preference thing, which, as we are all mature enough to see and understand, has no "right/wrong." No "better/worse" just "preferred/personally desired." Hence "Balance" really only exists (or is even "needed" at all!) insofar as the individual(s) playing want it/make it so.
Attempts to come up with some forced/created "balance" inbred into the system design is, as delricho stated, futile. And, not only "futile" but completely "made up", pulled from the ether by what the majority of the people concerned with it (designing the system) decide what "balance" means.
Again, I say, Bugaboo.
As always, have fun and happy [balanced?] gaming.
--Steel Dragons