Dedicated servers have always been popular and are the most dependable alternative. To run a website or some small services then it is definitely the way to go. then all the maintenance, monitoring, upgrades and backups will not be your problem.

If security is an issue or you want specialized hardware then start to look at colocation. in colocation, you keep your own physical server at a facility of the service provider.

I personally believe, for most applications, a dedicated hosting service of a reliable host like AEserver is the best option. Unless your needs are very unique, or you have extreme security needs.