I’m not so sure about whether this question belongs in this section or not, but here goes…
Is there any particular reason for there being so many Russians (or ex-USSR) who are so damn good at chess?
IIRC, Chess was one of the fields the Soviet leadership decided they had to prove their system was better at than that “ol’ evil corrupt capitalist” system is. Not to mention that it doesn’t require all that much in the way of funds for equipment, either.
Chess is the second most popular game in USSR, next to soccer. Where the US schools focus on football, the Soviets focus was and for the current CIS, is chess. Tchigorin was one of the first great teachers in the USSR, and his writings on chess is as entertaining as Grantland Rice on football. They were lucky to have other great teachers. Imagine the Collins Kids School in every city. That’s what the USSR and their satellites had.
The players they churn out may not be as instinctive as Pilsbury, Capablanca or Fischer, but they were not to be easily fooled.
As previous posters have noted, it was basically down to money, channelled through the Soviet Government for political kudos.
I think it effectively began before the Second World War, when the Soviets decided to reward chess players and thus become a world force. Talent spotters looked for likely juniors in schools, leading players were paid by the Government (as ‘journalists’ or ‘teachers’) and tournaments received massive publicity in the (State) press. Special schools for training were established and leading players were subsidised (provided they did well and thanked the State for their successes).
Alekhine, the current World Champion, died in 1946, and there was no provision for a replacement. You can already see the depth in Soviet chess as 3 (Botvinnik, Smyslov and Keres) of the 5 players who played the tournament for the title were products of their system.
Soviet players held the World title till 1972, till Fischer came along.
When I was a junior player (about 30 years ago), there were around 25,000 registered English players. The Soviets had about 8,000,000!
Garry Kasparov was spotted at School before he was 9 years old and given top quality lessons at the Botvinnik Chess School. (Kasparov now has his own Chess School.)
By contrast, my UK School didn’t have a chess club and I had to run the chess team as a pupil.
I didn’t get any official coaching till I was approached (aged 21) and asked to be a UK National Chess Coach. 
A large part of the reason why the US has so many good golfers is that there is a lot of money to be made from the sport - and so it is with Russian chess players.
Incidentally the Russia v the Rest of the World match is just finishing in Moscow. Results and commentary on:
www.kasparovchess.com
Um, Capablanca may have been rather lazy (he tended to play the same openings), but Fischer worked bl**dy hard. He would scour every available chess source (e.g. magazines) for the latest games and had a fantastic memory as well.
I’d also disagree about describing e.g. Tal as ‘not instinctive’!
I also don’t think any top player is ‘easily fooled’.