Depending on your router, disabling Ping can have a negative effect. If your router just ignores
ICMP Echo Request packets, all will be OK as described by @Layticia.
On the other hand, if your router ignores ALL
ICMP requests when you have disabled Ping, you could see several problems.
Your router must accept at least
ICMP types 0, 3 (all codes), 4, 5 (all codes), 11 (all codes) and 12 (all codes). Dropping these types can cause your link to become congested, and can cause vital processes such as 'Path MTU Discovery' to fail. In some cases, if PMTU Discovery fails, you can see a very reduced throughput on your link, dropped packets and connections or other issues which would affect the performance and stability of your connection.
ICMP is vital for congestion control and status messaging between internet hosts. There is little security benefit to disabling responses to
ICMP Echo Request packets, as there are other ways to determine whether a host is present on a give IP address.
See http://en.wikipedia.org/wiki/Internet_Control_Message_Protocol for information on
ICMP. See http://en.wikipedia.org/wiki/PMTU for details of Path MTU Discovery.