Counter or no-counter on an opening offer?

After over almost 2 decades in this industry, at times, I still fail to understand the endusers/buyers during negotiations and lose quite a few sales to the counter-strategy.

My question at hand is; Should we really counter to an opening offer or accept as it? What do most of you do?

So to build this discussion up and see what others have to say or suggest about this, recap on why I am interested to know what most of you do is because of this below mentioned situation/story:

Counter or no-counter on an opening offer?