Russia has always been against NATO and lately it is pushing hard for a strong SCO (Shanghai Cooperation Organisation) [1] which is branded as Russia's/China's answer to NATO.
The current major issue with SCO though is it needs either India or Pakistan or both as its members to make it a formidable military alliance. But since India and Pakistan are archrivals there are differences between Russia, which has always backed India, and China, which has always backed Pakistan.
[1] http://en.wikipedia.org/wiki/Shanghai_Cooperation_Organisati...