combinatorics - Combinational proof problem

I'm having trouble finding a combinatorial argument for

$\sum_{k=m}^n {k \choose m} = {n+1 \choose m+1}$

The right side is just choosing m+1 things from a set of n+1 things, but I can't see any way to relate this to the left side, where you're choosing m from m things, m from m+1 things, m from m+2 things and so on...