Can you play ds games on a nintendo 3ds?

I posted a question about the Dsi and the Dsi xl, but everyone is telling me if i get a system, to get the nintendo 3ds. My question is... Can you play regular ds games on that system? Im a HUGE Harvest Moon fan and i have all the ds games, that's why i was looking at the dsi or the xl. Are the games from my old nintendo ds interchangeable to the 3ds if i decide to get one of those? Thanks for you time and advice LEBE