I am re-routing a gas line in the crawl space under my house.

Is there any reason why I should not re-use the existing black pipe and galvanized pipe (and fittings) for the new gas line?

Also, is there any problem in re-using the existing ball valves for new gas appliances?

Of course I will be doing a pressure check for any leaks in the new gas line.

International Fuel Gas code prohibits the reuse of any Pipe, fittings, valves, or other materials.

International Fuel Gas Code 2012

Chapter 4 Gas Piping Installations

Section 403 Piping Materials

403.2 Used materials. Pipe, fittings, valves and other materials shall not be used again except where they are free of foreign materials and have been ascertained to be adequate for the service intended.

It also specifies not to reuse them in the installation instructions.

DO NOT reuse connectors, fittings and valves; they are designed for use on original installation only. Removal of connector and additional handling may damage connector making it unsafe for reuse.

Overall this is to help prevent leaks caused by dirt, debris, and damage that may prevent good connections. In this specific case, it's because the threads on the fittings involved are actually mashed together when the connection is made. This type of connection does not require pipe dope (which it also mentions in the installation instructions), since the seal is created when the threads get squished together. See the National Pipe Thread Fuel (NPTF) section of this answer for more detail.

Usually when replacing these type of fittings ("hoses"), you'll have to replace right back to the black pipe. If you have a valve with a flare end that the fitting ("hose") connects to, you'll want to replace the valve and fitting ("hose"). If there's an adapter with the flare, you'll replace the adapter and fitting ("hose"). Make sure you clean the threads of the black pipe really well, to insure there's no foreign material in the threads, before you connect the new fittings. You might also have to replace the flare fitting on the dryer as well.

The other problem with these fittings; though usually only fittings that have been in use for some time, is that they can actually be damaged when they are removed. Sometimes the threaded nut doesn't spin, and the pipe actually ends up twisting. This can cause damage to the pipe, and so it should not be reused in this case.