Is it possible RAM not compatible with Macbook Pro? As this is my first time dealing with HW of my Macbook Pro Early 2011 and need lot of money for service, I am quite nervous with this. 

I want to upgrade my Macbook Pro RAM to 8GB. What I can find from Apple website is the current spec:

4GB (two 2GB SO-DIMMs) of 1333MHz DDR3 SDRAM; supports up to 8GB


I want to buy this RAM which is written for Mac Apple:

Corsair SO-DIMM DDR3 8GB PC10666 - CMSA8GX3M2A1333C9


Should I go straight away since the spec is equal? I just want to evade the possibility breaking my Macbook Pro.
The RAM you listed there will work perfectly fine.
Whenever buying RAM just make sure you have the correct type (DDR3 in your case) and the correct speed (1333 MHz or PC10666 in your case).

It won't 'break' your MacBook but instead it just won't boot if you have the incorrect type or speed of RAM in your MacBook. RAM has no saved state when turning your computer off so logically it couldn't harm your MacBook if you switch it out for incorrect RAM and then put the correct one back in.

So summarized: The RAM you listed will work but in the future always check for speed &amp; type (I like to use MacTracker for this).