I downloaded the library from here, version 2: Arduino Playground - HomePage
The error was from using 1.5.6-r2-windows. I receive the following error using 1.0.5-r2-windows.
E:\Program Files (x86)\Arduino Uno\libraries\ICMPPing\ICMPPing.cpp: In member function 'void ICMPPing::receiveEchoReply(const ICMPEcho&, const IPAddress&, ICMPEchoReply&)':
E:\Program Files (x86)\Arduino Uno\libraries\ICMPPing\ICMPPing.cpp:177: error: invalid conversion from 'uint16_t' to 'volatile uint8_t*'
E:\Program Files (x86)\Arduino Uno\libraries\ICMPPing\ICMPPing.cpp:177: error: initializing argument 2 of 'void W5100Class::read_data(SOCKET, volatile uint8_t*, volatile uint8_t*, uint16_t)'
E:\Program Files (x86)\Arduino Uno\libraries\ICMPPing\ICMPPing.cpp:185: error: invalid conversion from 'uint16_t' to 'volatile uint8_t*'
E:\Program Files (x86)\Arduino Uno\libraries\ICMPPing\ICMPPing.cpp:185: error: initializing argument 2 of 'void W5100Class::read_data(SOCKET, volatile uint8_t*, volatile uint8_t*, uint16_t)'