Do there exist algorithms for which the Big-O cannot be found out? 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?
There are some algorithms for which, as of today, we are not able to prove termination, much less to bound complexity.

A simple case is given by the Collatz function: in pseudocode

function Collatz(n):
  if n &lt;= 1  then return 1
  if even n then return 1 + Collatz(n/2)
  return 1 + Collatz(3*n + 1)


It is believed that, for any natural $n$, Collatz(n) will eventually stop recursing. However, we do not know whether this is is the case. Consequently, we also do not know an upper bound for the time complexity of this algorithm.