Bare wood, or untreated wood, would normally be primed before painting. Most paints require a smooth, clean surface to perform optimally, and untreated wood is neither of these things. Unfinished wood is also very dry, which means your paint is likely to be soaked up quickly.

In short, if you were to paint onto wood without using a primer, it will probably take a few coats and may look fine. But if you want longevity out of your project and the best possible conclusion, use a primer first.