It's huge. It permeates all levels of the society. There are jokes, stereotypes and anecdotes that are essentially part of the culture. Most (if not all) of the people have at some point been subjected to them, and even if they are not antisemitic, they are certainly aware of the singling out of Jews.
This dates back to the days of the USSR, but the prejudice is not limited to Jews anymore. Chechens, Georgians, Tajiks, Ukrainians, etc. (even ethnicities indigenious to parts of Russia) -- all of them can be routinely discriminated against based on looks and/or name.
What has changed, though, is that the bulk of discrimination has shifted from the state to the people. E.g. folks are not discriminated against when trying to get into a college, but can be singled out on the street.
Note that with dissolution of the Soviet Union at least some republics - parts of Russia (e.g., Tatarstan, Bashkortostan) started to see discrimination against ethnical Russians. This increased movement of Russians closer to Moscow - or, say, to south-western parts of Russia, like Krasnodar region, with Russian majority.
Russia is huge and probably there are places that you comment describes accurately, but it is not so in my experience - most of the jokes about Jews I heard from a guy who is Jew and he don't seem to have any problems with his career.
I don't know. My well-off Jewish relatives in Russia don't report discrimination, but that I believe is a factor of their position or demeanor and not absence of antisemitism.
Since you asked "how big", I would say greater than zero but less than discrimination against certain other groups. These other groups include Chechens, other people from the Caucuses, people from the *stans, and gays. People in these groups are both more numerous and face worse discrimination. Non-Moscow residents are of course officially discriminated against in Moscow (Moscow residency is essentially a second internal citizenship that has been struck down by the courts but still exists in practice). Additionally 50% of the population are subjected to sexism to a significant degree.
Right now I'd say that being jewish is ok compared to some other nationalities, as there are quite a few reports of people murdered on the street in major cities for looking like immigrants from Caucasus or being black, but I haven't noticed such reports about jews.
If I visited Russia, do you supposed I'd experience more problems by being American or by being Jewish? Or would I even be likely to experience any problems at all?
Ha, what an interesting disagreement! One of the commentators said "it's huge", and I was just about to say that it is generally less than it used to be and has more of the legendary than practical status. Things can easily change back to what they used to be, but currently they seem to be okay. However, I need to mention that I have not lived in that country for 20 years now, and although have been visiting often, sometimes more than once a year, my view is not of the one who has to make a living there. I may not notice some undercurrents.
My impression (which is almost 100% from reading Ian Frasier's Travels in Siberia) is that nothing has a simple answer in Russia, and the question was probably ill-posed, but I appreciate everyone's reply. Even if the reports are contradictory, they help paint a picture.
