I've allowed dragon PCs in my 3.X game from the very start, using my own rules adapted from a long-ago 2nd Edition campaign that include the notion that PC Dragons advance age categories by gaining levels rather than waiting years of time (as it is in the Dragon articles). My Epic game has had three Dragon PCs at one time or another during its length, but the only current PC is one who's been with the party nearly from the beginning. She's gone from Wyrmling to Ancient in the space of a little over a year of game time (the game started at 1st, she joined around 4th level, and the PCs are now 31st-33rd with most being 32nd).
My experience is much the same as the other posters; a Dragon is pretty fearsome in low- to mid-levels with its built-in flight capability, natural weapons (and possibly ability to overcome Magic DR depending on level) and natural armor, and infinite-use area attack (the breath weapon). But the PCs keep pace if you balance the Dragon's power gain properly, and by 20th the Dragon actually starts to look a bit weak compared to the other PCs. That's because of several reasons, but the most obvious one is that Dragons take forever to gain the really high-level spells or psionics- whereas the other PC casters/manifesters are throwing them around from 18th or so onward.
While a Dragon PC can match a party Fighter in melee combat, the Fighter has a lot more feats, and thus more combat options available to use and abuse. Plus, the Fighter by 20th level will have weapons that can overcome many types of DR, while the Dragon PC is pretty much screwed unless the critter has simple Magic DR (or you give the Dragon a magic item to allow DR penetration of other types, which I did in my game to help out the PC- she was seriously becoming overshadowed by this issue).
The Dragon's mobility- meaning extreme ground speed and great flight speed (as well as built-in flight itself for that matter) becomes more or less irrelevant to the party travelling after about 13th level, when the party Wizard or Sorcerer almost certainly has Teleport for long-distance quests. Combat-wise, the flight means little when the party's standard practice is to give the Fighter a magic item or buffs allowing flight capability.
So yes, Dragon PCs are indeed balanced if done properly, and if anything it's a weak option when you reach the really high levels. RP-wise you can have a lot of fun with it though- my group certainly has! The Dragon PC's plot hooks have been the biggest plot generators for the party over the course of the game, and they're even now still cleaning up the civil war they helped start in Dragon society in my game world.