tcping — when firewalls eat your ICMP and you need to test port availability
arping — L2 diagnostics and duplicate IP detection, no IP stack needed
fping — scan a /24 in seconds, all hosts in parallel
OWAMP — when you actually need one-way latency, not just RTT
dnsping — when the slowness lives in your resolver, not the network
I put together a comparison table of the most useful ones, across protocol, OSI layer, platform, multi-host support, and root requirements. The OSI layer column alone tells you a lot — if you're reaching for ping to debug something that lives at L4 or L7, you're probably using the wrong tool.