Wow, something I can answer with some level of detail. My source for this is 1989: The Struggle to Create Post-Cold War Europe (Princeton Studies in International History and Politics).

So to your question. If you're trying to ask "Did the USSR collapse because the Berlin Wall fell?" the answer is no. It's not a causal relationship.

They are, however, related events. The way the USSR handled the fall of the Berlin Wall and the reunification of Germany reveals a bit about the weakened state of the political structures in the USSR. Keep in mind that Tienanmen Square happened in June 1989, and though it had been some time, the Soviets were not beyond sending in tanks to put down protests in Warsaw Pact countries.

So, in October\November 1989, when the East German government started to loosen restrictions on moving in and out of the country (essentially the result of flubbing up statements to the media), there was some concern that either the East German government or the Soviets would like they did in Prague 1968. None of that happened, neither did it happen when later in November the Czech Velvet Revolution came to pass (but that's a different subject). One could read this as a sign of weakness in the Soviet political machine.

Further during the negotiations to unify Germany (which I won't go into in too much detail here because I'm at work and my copy of this book is halfway across a continent at the moment), a couple of things stand out. There was a lot of contention about what the status of the East German state would be after the fall of the Berlin Wall, whether it would remain a separate state or reunify and whether such a reunified state would fall under the aegis of NATO or the Warsaw Pact. Obviously, the Soviets did not want NATO any further east than it already was, and throughout the negotiations to reunify Germany continued to insist upon a disputed promise that was made (I want to say it was the US Secretary of State James Baker) that NATO would not move an inch. There's something to be said about that dispute - from the US perspective, nothing got finalized in meetings, it was always a tentative agreement until it could be approved by the administration at home. Gorbachev's perspective was the opposite, that the meetings were where the deals were happening (which speaks some to his style of governance - many in the Soviet elite felt they were being cut out of decision-making and grew resentful). Eventually, Gorbachev was convinced to drop these objections in the face of a large sum of money (again, I don't have the book near me) to be paid by West Germany to the USSR. This again points to a weakened political system.

In short, there are a ton of reasons why the USSR fell apart. The Berlin Wall was probably not a direct contributor to that process, but it does point us toward some important things that were.