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.

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.

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.