My answer is usually "is your brick ugly ?"
If it is then yes paint your brick. I do love a painted brick house so much so that when buying a house I am generally only attracted to an ugly brick house that needs paint. I know I have issues but truly I have rarely left a house Unpainted.
I use two different types of products Benjamin Moore exterior paint the Aura line since it gives a great sheen or Boral Brick Re-Cote Product that has a thick sand like finish that should be rolled on and feathered into the brick. See house below where we used the Boral product.
The house below was a handsome house but I thought the brick was a little orange for the roof color which had a green undertone. Although I love a White House this roof color was better suited for a creme colored paint on the brick. Gas lanterns were added and one set of columns removed. The columns doubled kept you from seeing the new gas lanterns and newly added front door. The original door was a metal door with side lights. Not attractive right? So with a single door with sidelights you have room to do a double door. We had one custom Made out of cypress. Such a beautiful wood and makes the front of the house so much more attractive. Also brought in much needed light for the foyer.
So next time you buy a house with ugly brick or already own one don't be scared to paint the brick. Painted brick is beautiful.
Happy Friday Y'all
Love Where You Live