how to stop water leakage where a vertical and horizontal stone wall joins?

The type of repair depends on whether the joint is accessible from the outside or inside and if the leak is migrating through the joint or getting into the wall and leakingin at the joint. If you can access the joint from the outside then I would suggest that you clean out the joint and make the repair from the outside. I would generally say to use a polyurethane caulking to fill the joint and right after you tool it throw dry sand into it to replicate the mortar. IF you think that the water is getting in at the joint this is a good fix, but if the water is getting in elsewhere then showing up at the joint this repair might trap the water and not allow it to weep out.

If you see water at the interior and you can get to it, try using Thoro Waterstop to stop the leak. Clean out the joint with a hammer and chisel and fill it with a mix of waterstop. This is a good material and will stop the active leak.

To give you some added insurance do both repairs to keep the water out or the wall and to seal the interior.

If this does not deal with it, you might want to clean and seal the entire wall with a Siloxane water repellant to seal the joints against water intrusion. These repairs ought to help solve the problem.

http://www.ehow.com/how_14426_repair-masonry.html