There are two problems with ping,
- On some networks they are filtered; so you cannot get a response
- On a busy network it can dropped in favor of higher priority traffic, it is annoying because it can generate numerous false positives
That being said, I would start implementing some basic monitoring using ping or a ssh/telnet session to check running processes on a box. I have looked at SNMP and I find that it is overly complicated and was not really worth the time invested; It was easier to just capture the output from a ps -ef command and parse that to see what was going on.