Security issues, especially if enabled on the serial interfaces.

How to disable CDP globally ?
no cdp run
How to disable CDP per interface ?
int s0/0
no cdp enable

Many tools to exploit Cisco CDP. For example some of these tools can generate a large number of CDP (multicast ) packets and fool other Cisco routers / switches into thinking that they are connected to 1000s of other Cisco devices.

While very useful for network management, this can lead to information leak by letting hackers/ intruders query your devices using CDP !