Is there a utility that works in the background and is able to notify me if my computer is being pinged?
2 Answers
Ping packets are actually ICMP echo request packets. You can check wikipedia to better understand.
As RedGrittyBrick sayed, this is often a part of Firewall applications. You can however try to block ICMP requests through your home router and watch the log for detected ICMP echo requests.
windump (tcpdump for windows) will tell you everything you want to know about any pings your NIC receives.