Universal One-Way Functions
That is an interesting question since there is no proof that one way functions exist. There is a lecture about this from Cornell's Cryptography course by Rafael Pass  which can be found here

To summarize the lecture:  


If one way functions exist then $P\neq NP$.  
There exists a function $f_{UNIV}$ such that if there exists any one-way function, then $f_{UNIV}$ is a one-way function.  Thus $f_{UNIV}$ can be considered a universal one-way function.
$f_{UNIV}$ works by acting on all Turing machines after $n^2$ steps of execution.  It is defined as

$$f_{UNIV}=M_1^{(|x|^2)}(x)||M_2^{(|x|^2)}(x)||\dots M_{|x|}^{(|x|^2)}(x)$$

where $M_{i}^{(|x|^2)}(x)$ denotes the output of Turing machine $M_i$ on input $x$ right after $|x|^2$ steps of computation.  
If a one way function $f$ exists it can be solved by a Turing machine $M$, which will be polynomial solvable by $f_{UNIV}$.


Caution: the construction of $f_{UNIV}$ is in no way practical.  This is about asymptotic complexity, not practical security.