Michael Bohm has an interesting article in the Moscow Times summarizing the ambiguous and contested nature of national identity in Russia. The problem is that in the Soviet Union the state cultivated a supra-national identity: New Soviet Man. Some of that tradition carried over under Boris Yeltsin, who promoted an ethnically neutral civic identity. One step in that direction was the abolition in 1997 of the ‘fifth paragraph’ on identity cards which recorded each person’s ethnicity.
Non-ethnic Russians make up 20 percent of the population of the Russian Federation, and some of the minority ethnic groups, such as the Tatars, objected to the removal of the fifth paragraph, arguing that it would lead to the erosion of their language and culture.
Russian nationalists complain that the ethnic ‘neutrality’ of the Russian state works to the disadvantage of the ethnic Russians. They argue that the 21 ethnic republics within the Russian Federation, which enjoy a fair degree of autonomy, unfairly benefit from generous federal subsidies and tax breaks. Some also complain that vote-rigging in the ethnic republics heavily favors United Russia and President Putin. See for example this September 8 speech by the leading Russian nationalist Dmitry Rogozin in which he calls for the ‘renationalization’ of the Russian people (in Russian).
Most of these complaints are targeted at the North Caucasus, where ethnic conflict and terrorism has spilled over from Chechnya into Ingushetiya, North Ossetia and especially Dagestan. Some are even suggesting that Russia should withdraw completely from the North Caucasus. See for example these clips from the campaign “Enough with feeding the Caucasus!” (in Russian). For analytical background see this March 2011 report from the CSIS The North Caucasus; Russia’s Volatile Frontier, discussed at this roundtable.
In addition to the ethnic minorities who are Russian citizens, Russia is home to some 10 million immigrants from the former Soviet Union, mainly from Central Asia and the Caucasus, who are drawn to work in cities like Moscow and St. Petersburg which are short of labor. (Russia has the second-highest number of immigrants in the world, after the US.) These immigrants are regularly the target of racist assaults, as documented by the Sova Center.
This general disaffection about the state of Russian identity is not politically threatening unless and until some groups are able to mobilize it for political purposes. There are two focal points for such mobilization: elections, and protests that flare up as a result of antagonism towards ethnic minorities and migrants. The Kremlin has been able to neutralize xenophobic parties by creating their own nationalist movements, and by tightly controlling the registration and leadership of parties allowed to compete in State Duma elections.
On the Kremlin’s manipulation of nationalism, see this recent oped by Vladimir Ryzhkov. I discussed the radical nationalist fringe groups in an earlier post, and I have a book chapter analyzing the course of nationality policy under Putin.
nationalismwatch 
This is a very interesting overview of Russian Nationalism under new challenges. In a political experiment where great Russian nationalism
overshadowed the other ethnic nationalisms for decades, and nationalities demands were considered as ‘ vopros’ or issues under
question, the new turns are rather obvious and unavoidable. The new Russia must handle the demands of each nationalities with care so that this doesn’t turn into ethnic tug of war on various layers.
Along with this tensions over national identities on the very material ground, one wonders the position taken by the Russian state over the
trans-border nationalism, nurtured and furnished by a new genre of immigrant Russian intellectuals, situated in different parts of the
west, USA, Germany or France. Many of them carrying Jewish identities have bitter experience of Soviet purges at particular historical
moments. Still they carry their Russian selves, sometimes, even Soviet upbringings within their rehabilitated dual entities. How is their
reception to the transformed Russian state? Will they be recognised as an important category of Russians, repatriated, at least theoretically
to their land of origin at least for their cultural contribution or emotional commitment to the Great Russian land?