Usually .pdb files are not shipped to a client, but they should be kept for every released build in the developer company. Having these files, you can debug crush dumps from a client computers.
Important note: for Microsoft projects, it is impossible just to rebuild the same source code and use .pdb files from the build. .pdb files should be the same files that where created when release was built. Microsoft uses UIDs to match exe and .pdb files, if there is no match, debugging symbols are not loaded.
Shipping .pdb files to a client is harmless, but also useless, unless you can make debugging directly on client computer.