Which is why his reply was directed at rainydays, who does want to turn it off. 😉
Now, to address your question:
First, as mentioned, check and double check that your volume is not muted. Do you use external speakers? If so, make sure everything is connected properly and/or unplug them completely to try just the internal speakers.
The POST chime is an important indication that your machine is working correctly, so yes, you should care if you don't hear the chime and your speakers are not muted.