Oh man, I had the same thing. I agree with Gotry it–check out the roof and gutters first. If they check out, repointing is probably the way to go. If you are repointing yourself, make sure to use the correct mortar made with lime. If you use a mortar with cement in it, it will shred your bricks and you will have even more leaks.
If your house has not been repointed, then you may want to look into it. Bricks need to be repointed about every 100 years or so. If you decide to do this, make sure to check out the PoP post for recommendations on masons: http://www.popville.com/2011/02/dear-pop-repointing-an-end-unit-townhouse/
Vinyl siding would probably also be a feasible alternative, but you may want to have someone check out the bricks anyway. Repointing may not be as expensive as you think, and a mason couild let you know if there’s any danger of the bricks falling out or something like that.