http://en.wikipedia.org/wiki/Battle_of_Grozny_(1994-1995)
During the opening stages of the First Chechen War, the Russians launched a poorly planned assault on the city of Grozny. While they were eventually victorious, they lost more than a thousand men and hundreds of tanks. Almost half of their armored vehicle losses happened in the first day of combat, when four huge armored columns attempted to storm the city without adequate preparation and very little (if any) infantry support.
It has been known since World War Two that armored vehicles become vulnerable in the close quarters of an urban battlefield. In fact, the Russians were the ones who proved this most decisively when they sucked German armored forces into places like Stalingrad. This principle became even more acute after the introduction of cheap, highly effective anti-tank missiles. And these principles become even worse if your enemy knows where your tanks weak spots are, as the Chechen fighters (many of whom were veterans of the Russian military) did. It's suicide to send tanks into a city unsupported by infantry, and the Russians knew this.
So why did they do it?
Basically the Chechens had made the requisite preparations by blocking streets and setting up ambushes. This made the columns' advance uneven, with at least one getting bogged down in a firefight, even as other Russian columns were still making progress. Then, there was not enough (ready) forces or command initiative to rescue the column that had been trapped. And the other columns' progress also began to suffer a similar fate.
The reasons for this seem mostly to be the organization and doctrine of the Russian army at the time. The army's leadership was very tightly controlled by the political leadership, so that the assault's overall strategy was bent on political goals rather than strategic ones. As you may imagine, military domestic action is a fairly touchy political proposition. The political leadership wanted the entire Chechen situation resolved quickly, and the Russian army was poorly equipped for fighting an insurgency. The Berlin analogy isn't a bad one, since that is basically what Grozny devolved after the initial assault failed.
Another factor was the disconnect between the army and the FSB, which understood the situation on the ground probably a bit better than army intelligence (GRU) did, but likely had conflicting interests in the region, and, generally, has always been the army's direct political rival in Russia.