Superficial cracks in brick aren't much of a concern, and can be left as is. Cracks that are a little wider than this also aren't cause for concern. If they bother you, you can touch them up with grout tinted to match the color of the brick.
If you have brick that's cracked all the way through, it should be replaced. This is best left to a bricklayer, especially if the damage is extensive.
As mentioned in How Brick Crumbles, waterproofing can be applied to brick surfaces to slow down spalling. Keeping weep holes clear in brick veneer will also help eliminate some water problems. Unfortunately, this is easier said than done, as weep holes are often clogged with mortar that's dropped by the bricklayers during the building process. If this is the case, it's possible to have special vents installed to improve ventilation. These vents are the size of a brick and are held in place with caulking.
Mitigating Mortar Problems
Even the best mortar will break down over time. The lime in it leaches out, cracks develop, and water seeps in. When this happens, mortar starts to crumble.
As mentioned, you can replace crumbling mortar by repointing it. You'll need the following:
A chisel or similarly pointed tool.
Mortar. You want dry, ready-mixed mortar. Buy a bag marked water-resistant type N.
Something to mix the mortar in. A plastic bucket (plan on throwing it away when you're done) is fine.
A small trowel.
A spray bottle full of water.
Here's what you'll do:
Don your goggles and use the chisel to chip out the old mortar.
Mix the mortar according to the package directions.
Dampen the area you're going to work on slightly with the spray bottle. Doing this will help keep the moisture in the mortar you're applying from migrating to the surrounding areas, which could result in mortar failure due to insufficient moisture.
Pick up a good amount of the mortar on the trowel and pack it into place.
Firmly press or pack the mortar into place with the flat edge of the trowel. Try to match how the mortar is finished in other areas. Slide the trowel along the wall to remove excess mortar.
Clean any additional excess from the wall.
Keep the repaired area damp for three to four days while the mortar cures.