Migrants from Central Asia and Eastern Europe work in Russia and send money back to their families. This is so common that the economy of many of these countries is dependent on the remittances. With the value of the rouble falling so quickly, these countries will also experience instability.
Importers to Russia such as Germany and China will also be detrimentally affected by the economic turbulence.
A collapse of the Russian financial industry would cause great havoc worldwide in that the ability of Russian banks, and even the government, to repay outstanding financial obligations would be impaired. In many cases the failure to repay notes due on a timely basis would result in defaults and the forced unwinding to trades and company purchases.
The Russian economic collapse is not healthy, but was instigated through other means, therefore it was not a natural collapse, but a coerced one. Other currencies are not tied to the ruble like the dollar and not all countries trade with Russian either, so the impact will not be as extensive if the dollar collapsed. It doesn't help trade, but not all countries will be affected by this.
If Russia were to ever suffer a massive financial collapse, I think it could cause issues with the economy, but I would not go as far as saying "world wide". Certain countries that partially depend on Russia may be in trouble, but they would not be "lost" without the financial assistance of that great country.