http://aremysitesup.com/ offers a free plan with 15 minute interval checking, or a paid plan (from $5.42/month) for 5 minute interval checking.
If you're just monitoring one site, pingdom's free account offers 1-minute interval checking -- you just need to login once every 90 days to keep it alive: https://www.pingdom.com/signup/free/ (If you're monitoring more than one site, their prices are pretty reasonable, in my opinion.)
If you're really concerned with uptime you might also like to consider DNS hosting with a DNS failover service, which monitors your site every 2 to 4 minutes and updates your DNS to point to a backup server should it find that your primary server is down. Of course, this means you need to pay for a backup server, and that you need to mirror the content between the two servers.
(I'm not affiliated with any of these services, though I've used all of them for different projects.)