Is it needed to use thermal paste when...?

You always need some sort of thermal compound between the CPU and the heatsink, the one that comes with the CPU will generally have a pad preapplied but if you ever remove the heatsink you should clean it off and apply new paste. Most aftermarket coolers will come with some thermal paste, you can use that or you can buy other stuff, but you do need to use paste.
 
The stock cooler (standard) will have a thermal pad on the heat sink already.
There is no need to use thermal paste with this, just fit the cooler following the included instructions.

If you buy an aftermarket cooler, it will also come with a thermal pad or thermal paste.
You do not need to purchase additional thermal paste.
Instructions should be included.
If there is a pad fitted to the heatsink, just fit the heatsink.
If the heatsink has a clean surface, you need to apply the supplied thermal paste.
This is usually applied to the CPU, but some instructions will say to apply to the heatsink instead.
 


You mean, though I don't have to use it if I use the standard one, to have thermal paste just in case I need to remove it?

The truth is that I asked this because that's such a hard task >.< (not in that way, I mean, what if you put too much? and what if you don't put enough?)
 


When people fit aftermarket coolers on graphics cards they also need to use thermal paste.
If you use the stock CPU cooler and leave the graphics card with its original cooler, you won't need to use thermal paste for anything.
 


Use the standard coolers.
This will save you money and the hassle of fitting an aftermarket cooler.
Standard coolers are fine without overclocking.