There are many reasons why people do it:
1. You can install anything you want in regard to scripting languages (ntl webspace doesnt provide php or anything like that).
2. If it goes wrong its your fault, not ntl's or you hosting ISP's.
3. It is easier to update by simply sending your site via a network drive rather than waiting forever to transfer it by ftp.
4. You gather experience from running a webserver.
5. Resources are dedicated so it is a lot faster than shared hosting.
There are many more reasons but I cannot think of them all.
The only downside is that it costs roughly 34p a day for me to run my webserver, that amounts to about £120 a year. Its a lot more than paid hosting but it makes up for itself with the ability to have whatever you like on it.
My website is designed for helping people set up servers on their internet connection (not just on ntl, on any isp).
If you want to take a look its
www.abyssunderground.co.uk.
Also, I do not use Apache. I use a much better server called Abyss Web Server. Ill explain more if people want to know.