If you're shared hosting plan is like mine, and they guarantee 99.9% uptime, I HIGHLY recommend you signup for a free Pingdom.com account.
So you can set it up to monitor your websites uptime, and it'll generate a report which you can fire off to your host when they fail to meet the 99.9% guarantee. Moreover it'll email you when your site goes down so you can bug the host to fix the problem.
**DISCLAIMER**
I am not at all affiliated with pingdom, I just love the service.
2019 EDIT
Pingdom is now a paid service, still good, but not as "Free"