Nearly all web hosts will advertise and guarantee a "99.9%" or higher uptime percentage. However, these guarantees are about as trustworthy as a used car salesman, not very! If a host has a history of a great uptime performance they will post a history of their uptime performance, monitored by a 3rd party, such as Alertra or InternetSeer.
Additionally, web hosts that operates on a redundant network (more than one data line to the internet) will be more reliable than a web host that is running only a single data line.
Monitor Server Uptime
If you have already signed up for a web host you can use a 3rd party to constantly monitor your site's uptime and be instantly notified by email if your web site ever becomes unresponsive. InternetSeer provides a free monitoring system that will check your web site every 60 minutes. If your web site needs to be monitored more closely, both Alertra or InternetSeer have pay for monitoring plans that are very thorough.