That depends on the power your sub needs and how much power your head unit (stereo) supplies. In most cases you need an amp, in even more cases it is just best to have an amp because not only are you less likely to blow your sub, but your sound will be much cleaner too.
So short answer- Yes, you need an amp to run a sub.
There are powered subwoofers like the Basslink which might be an option for you. You don't have to mess with as much wiring or a separate amp. Depends on the goal you have for your system. Big booming bass, bass fill, etc. A "real" subwoofer/amp combo will generally be of better quality sonically but something like the Basslink can complement a stock system nicely without a lot of the hassle of separate components.