Don't make the mistake of thinking you can walk into a Russian building wearing your street shoes... People won't think twice about reprimanding you for your bad manners. Many places put two baskets next the entrance: one containing unused shoe covers (bakhili/бахили), and one for dirty pairs. You'll usually find bakhili at schools, hospitals and gyms -- but not in restaurants or stores.
I must add that it's important to remember to take them off before leaving... Otherwise you'll slip as soon you set foot onto icy pavement... And you'll also look like a complete idiot. Especially if you end up walking around for a few hours without realizing you're wearing bright blue garbage bags on your feet. Trust me.
Natalia's kindergarten was quite clever: they painted a toy chest gold and made it look like a treasure chest full of the ubiquitous blue covers.
When I had to go to a Russian hospital last week for a catscan, I had fight the urge to whip out my camera so I could take a picture of the gumball machine that dispensed pairs of bakhili! People entering the hospital had to buy their shoes covers for 10 rubles and 50 kopeks. Who carries kopeks around these days?! Sure, add one more thing for worried families in the emergency room to have to deal with... Scrambling around for esoteric coins so they're allowed to walk on the floor...
Wait... Ah hah! (I'm now finishing this post a day later). I had to back to two more hospitals today (more on that later) and I did get a picture! At this hospital, however, they cost 10 rubles even.
Our school provides bakhili for all visitors, but students and faculty are expected to keep all outerwear strictly in the coat rooms (heaven forbid a scarf pass along a germ...) and everyone brings separate shoes for indoor wear only. It can be a real pain, but it does keep your nice shoes looking, well, nice...
The whole indoor/outdoor shoe thing leads to very odd shoe choices for the younger kids... They end up with one pair of indoor shoes that stays at school -- and certainly doesn't go with a wide range of outfits. Most kids just wear sandals all year round, strapped over their thick Russian tights. Katya has a pair of mary jane black sneakers; Natalia prefers her sparkly purple mary jane Crocs.