Just out of curiosity:

Do there exist algorithms for which the Big-O cannot be found out?

I have done a quick search in the google search bar:
"Big o, impossible to evaluate"
"algorithms without big o"

And these gave results which were unsatisfactory. Mostly, teaching me how to find the big o. Nothing I haven't learned earlier. 

On a side note, it is my understanding that finding the big o requires us to assume the worst possible case. But, is that always a correct metric for efficiency? What is the likelihood a function is called with the worst possible argument?