Not really.

From what I've seen, unless you're allergic to something in the brick (lime, mortar), there's no real benefit other than controlling the mortar (if it's crumbling and in need of repointing) or changing the color. Depending on the brick, the texture and color create a major impact on your overall design. A recent project I've worked on has a non-supportive brick column with no fireplace. It's absolutely huge. As a flashed red brick, it dated what the customer wanted to update about the space (she wanted a contemporary feeling) so painting it kept the cost down while improving the feel of the space. I'm not saying flashed red brick will date your space, but whatever color is chosen needs to corroborate with the rest of your design. Functionally, there is no real reason to need to paint brick. Traditionally, it is a fired clay at such a high temperature that it will weather nearly any environment. At the end of the day, it's your call.