Given $f$, does there exist $f_t$ with $f_t(f_{t'}) = f_{t+t'}$ and $f_1 = f$?

Question

Suppose I have a map $f:X\to X$ on some reasonable space $X$. (I'm particularly thinking about a smooth map on a compact manifold or a homeomorphism of a compact CW-complex, but feel free to work in whatever category is convenient.) How can I determine whether there exists a flow $f_t$ on $X$ with $f_1 = f$; that is, a function $f_t(x):\mathbb{R}^{\geq 0} \times X \to X$ (in the same smoothness category as $f$) with $f_t(f_{t'}) = f_{t+t'}$? Obviously I need $f$ to be homotopic to the identity; is that sufficent?