Fastest way to ping a network range and return responsive hosts?

You should use NMAP:

nmap -T5 -sP 192.168.0.0-255

The following (evil) code runs more than TWICE as fast as the nmap method

for i in {1..254} ;do (ping 192.168.1.$i -c 1 -w 5  >/dev/null && echo "192.168.1.$i" &) ;done

takes around 10 seconds, where the standard nmap

nmap -sP 192.168.1.1-254

takes 25 seconds...