There is a stereotype that dates back to the Cold War that the Russians never threw away anything of utility. Behind this stereotype is a notion that somehow the Russians were keeping this war material as a back-up just in case war broke out. As with many stereotypes, there's some validity to this, and I would add, many nation-states are reluctant to scrap or recycle expensive military hardware (look at the tone about government waste in this Reuters piece- US planes worth $500mn sold for scrap in Afghanistan – for just $32,000 - even though this particular procurement was quite flawed, a lot of the animus in the headline surrounds the scrapping). However, in the case of Russian air power, the reserves of aircraft have a more mundane reality to them. The 1990s were a period of great fiscal cutbacks and drawing down of force structures for Russian aviation. The VVS (the air force proper) merged with the VPVO (air defense forces) in 1998, but this amalgamation led to a significant downsizing of the delivery of aircraft. The VVS took delivery of only 77 new aircraft in 1992, and the numbers shrank from there- 66 in 1993, 29 in 1994, 31 in 1995, 19 in 1996, 6 in 1997, and 0 in 1998 (mods- sorry for breaking the twenty-year rule- that zero number was just to juicy to leave out!). In contrast, the 1980s saw deliveries of new aircraft average to about 400 planes per annum. Although many of the successor states inherited some of the Soviet Air Force, these reserves of aircraft were used to keep the active squadrons flying. Many Russian commentators disparaged the reliance upon cannibalization of older airframes as detrimental to safety, but the practice became quite widespread within the VVS during these lean years. The VVS-VPVO merger also complicated matters as not all of their equipment was interchangeable- some aircraft like the MiG-23 had dedicated interceptor variants with specialized avionics. This gave a further impetus to keep large stocks of aircraft in reserve.

Edit: one other thing to add is that disposal and recycling of military aircraft is often a different matter than civilian aircraft. Military airframes sometimes use different types and qualities of material that have less of a market value. By the same token, parting out obsolete aircraft is a different matter than civilian as military equipment is highly specialized (there's not many buyers for ejection seats in the airlines) and subject to resale restrictions. Plus air forces serve as their own internal market for retired aircraft parts. The result is that the husks of military aircraft often rust away since the cost of scrapping often exceeds the value of doing so- this short University of Oxford paper-PDF warning explores some of the issues facing the recycling of civilian aircraft.

Sources

Lambeth, Benjamin S. Russia's Air Power at the Crossroads. Santa Monica: RAND, 1996.

_. The Continuing Crisis of Russian Air Power paper. RAND Corp, Santa Monica CA, 2001.

Many were sold or passed on to succesor states (Kazachstan, Eastern Europe, etc.) after the fall of the Soviet Union.

More than 10,000 MIG-21's were built, but are no longer in use by Russia, and most Warsaw Pact countries have also replaced them. Being a somewhat outdated, but useful aircraft, they have been sold en-masse to Asian and African countries, of which some still operate them today, but they are heavily outdated. Many countries have already replaced them. They are too obsolete to be efficient, and thus, i can only determine that they've been scrapped.

The MIG-21 and 23 series were mostly multi-purpose aircraft, with some deviations, but are outdated. After the fall of the Soviet Union, those that were still in Warsaw Pact countries were simply left there, others sold off, perhaps some scrapped. Neither of these are in use by Russia today, having instead replaced them with the newer MIG-29 (which is fairly comparable to a F-15 Eagle in performance) but are also a lot more expensive. As such, there are far fewer numbers than its predecessors. Many of those are also exported, mostly to the Middle-east and North-Africa.

However, the more specialized aircraft (Interceptors, close air support, reconnaisance) of the MIG series are stored or in use by Russia. All in all, we can only guess how much. But i think that ~1500 - 2000 in storage of them is a decent guess.

So, to answer your question: Yes, there are still a whole bunch of 'em stored. How many? We have no idea.