The ones digit of $ 3^1 $ is 3, the ones digit of $ 3^3 $ is 7, the ones digit of $ 3^5 $ is 3, the ones digit of $ 3^7 $ is 7, and so on. Write ``$ \equiv $'' to mean ``has the same ones digit as.'' Then \begin{align*} 3^1+3^3+\cdots+3^{2009}&\equiv 3 + 7 + 3 + 7 + \cdots + 3 + 7 + 3 \\ &\equiv 0 + 0 + \cdots + 0 + 3 \\ &=\boxed{3}.\end{align*}