The real line $\langle\mathbb{R},\lt\rangle$ is (up to isomorphism) the unique nonempty, separable, complete, dense, endless total order. 

(All conditions are needed: Without *separable* we have for example $[0,1]\times\Bbb R$ with lexicographic order, without *complete* we have $\Bbb Q$, without *dense* we have  $\Bbb Z$, without *endless* we have $[0,1]$, all with standard order)