Well, lets start by going through the various definitions of "broken":
Broken = "too good to pass up" - the idea that any team without a certain Pokemon/other game element can be improved by adding it. I don't like this definition, as under it Protect is broken, and possibly Fake Out and Intimidate too. I doubt Thundurus is broken under this definition, as other teams may require different or more specialised forms of support.
Broken = "too easy to use" - this is a bit better: timing Protects and outwitting your opponent requires skill. I would also say that Thundurus is very easy to use, just spam Thunder Wave on opposing sweepers and Taunt on opposing supporters.
Broken = "impossible to stop doing what it is supposed to do" - the argument used to ban Froslass from UU recently, and before that Deo-D from OU. Also the main reason for the discussion of U-Turn in singles - you can't stop it from winning a prediction war and switching into a counter. Apart from natural paralysis immunity/Lum Berry, all the ways of preventing paralysis are blocked by Prankster+Taunt (Safeguard, Substitute, Taunting Thundurus). So yeah, Thundurus can definitely cripple your entire team, and is broken on this score.
Broken = "overcentralising" - the metagame revolves significantly around the broken object and its counters. Well, Stealth Rock is broken in singles on this score, having developed counter-measures (Rapid Spin), counter-counter measures (spinblocking), counter-counter-counter measures (Foresight, Pursuit), and even counter-counter-counter-counter-measures (double ghost cores). Maybe the metagame is too young but a spike in Magic Coat and Mamoswine usage might convince me that Thundurus is overcentralising, and thus broken. The degree to which the recent Ubers suspect ladder revolved around Darkrai convinces me that, without Sleep Clause, sleep is broken (sorry VGC-ers, but in doubles you're even LESS likely to ever get a sleeping mon awake again).
Broken = "relies solely on luck" - not too much of this about, i could take arguments about Teeter Dance being broken. Luck-based stuff is mostly banned anyway - please add Brightpowder to future versions of Evasion Clause.
So, it's difficult to say. Is a broken Pokemon a Pokemon that displays all of these traits, or one particular trait, or a certain number of these traits? It is difficult to say. But I will say that it is VERY hard to stop Thundurus crippling most of the opposition - most of the time, you need good prediction (as with many things in doubles), and, at the end of the day, that often ends up being a coin-flip.