I actually work with managed servers.

The website, support system and licensing database for who I work for is on a bank of servers halfway around the world from me in RackSpace. Although we do a lot of custom configuration, they are extremely responsive and can do quite a bit of trouble-shooting at literally any time. I can request a box to be rebooted and it will be done within about 20 minutes, usually quicker. Of course, we pay for all this, but we have over 25 machines, most behind a dedicated load-balancer, as well as three quad Opteron machines with 8Gb of RAM as our databases. Hardware is usually Dell and there is a wide range. Without sounding like an ad for them, RackSpace can setup and run the box for you in whatever redundant arrangement suits your application and all you have to do is run your app. Since we look after the OS ourselves, we probably pay too much. But their support is stellar, which is probably why we went with them. They would be a top-shelf hosting setup.

We also have a few dozen boxes at an outfit called The Planet. They are rather less responsive and we pay correspondingly less. However, they have a remote console interface and a remote power interface, so you can theoretically reboot your machines yourself. I know commodity hardware to do this exists, but it gets pricey quickly. Colos obviously have to recover that cost.

I looked at a cheaper hosting company for my own website and domain, since I was wondering at one point if I could do that and go to a cheaper DSL service (turned out that would be more expensive than staying on my static IP DSL). One that I found advertising on Kuro5hin had a range of virtual machines at the low end to real hardware on the high end. Some of the virtual machines were for extremely specific applications: DNS and secondary mail queues was one. But that's usually a low-traffic situation.

There are also companies that host specific types of applications. They provide the hardware, the OS, the app - you provide the customisations to your instance. LiveJournal do this for blogs. I also worked briefly for a company that did that for e-commerver. They basically rented space out on their e-commerce web-servers. And don't think they're limited to small volume: where I work for now uses just such a service for our shopping cart and purchasing. And we're not their biggest customer!