Vigil is an easy-to-use, inexpensive website monitoring app for iOS. I've been using Vigil for the past few months to monitor 16 sites. It has notified me of two separate issues during that time: a bandwidth overage for a Wordpress site and a (user managed) SSL certificate expiration. About a month ago I did receive a couple of notifications in error, but the Vigil twitter account did a good job of communicating the problems they were having. That is the only issue I've encountered with the service, and it was a minor one.
The only feature I wish Vigil included is access to more historical data; currently only the previous hour's response time data is viewable. It would be nice to be able to see a detailed history, maybe even with an option to export the the data. They are apparently developing some kind of "more detailed history view" for a future version:
@iain It is not possible in the client currently, but we are working on adding more detailed history views for the next major release.— Vigil App (@vigilapp) April 15, 2013
The thing that first caught my eye about the service was the price: $9.99 for a year of monitoring an "unlimited" number of websites. That is extremely affordable. For comparison, the cheapest plan at Pingdom monitors up to 10 sites for $9.95 / month. It was a no-brainer to try out, and I'm extrememly glad that I did.