I get you mean a networking IP address rather than a completely separate internet IP address. The only reason for a static IP for the web is to run a web server.
When networking, it is a lot easier to have a static IP if you are labelling machines, i.e. printers and computers. It connects quicker as well. Takes longer to set up but if there's a problem then you can find the computer by the IP address on the network.
So overall:
Pros
------
- Easier to find computers
- Quicker connection
- Each machine is unique
- Easier to set up firewall settings
- Can create workgroups etc.
- Easier to maintain
- Less to go wrong
- Easier to diagnose and use network settings
Cons
-------
- Longer to set up
- Possible interference if you don't set up correctly and document the addresses used
So I would make them static, and document properly. Hope this helps.