In Moscow/St. Petersburg, people who do this are called diggers (the English word intact). Media, especially tabloids, love them and surround them with a mysterious aura. Time and again, stories pop up about the secret redundant metro, Stalin-era bunkers or catacombs that remember the days of Ivan the Terrible.
I, myself, explored the not-so-crowded areas of the vast Main Building at the Moscow University during my studentship there. Those who've seen Brazil can get a glimpse of this place's magic. It's true that this building spans many storeys down under the ground in addition to its 35 "official" ones. I only made it to the inhabited upper levels, where some cryogenic lab grunts can be found doing their murky deed, and mains hum away (I wanted to climb further down, but a distant "Fresh meat!" reached my ears, and I changed my mind). The entire university complex's got to be interconnected with passages, albeit closed for the peacetime; roomy bomb shelters are provided as well. The tower top is also quite interesting: submarine-style oval doors and steep spiral stairs, head-spinning views upon the city here and there, an ancient elevator for the topmost floors, opening before massive locked doors at some positions — there are classified communication facilities in the tower. I was nearly locked upstairs once. Today all I've got to do is to read Harry Potter.