Well... not really, but that doesn't mean having your own server set up isn't cool. A shared hosting plan is what most people start out with when they build their own website, and for most purposes that's really all they need. The type of sites I typically build are perfect for a shared hosting environment, they're low traffic and don't use much resources.
Despite the fact that I really don't have a pressing need for a virtual private server or VPS, I ran out and signed up for one anyways. It gives me something to tinker with and the price wasn't that much more than what a shared host would cost. The upside to having one is that you can configure it anyway you please. You don't have to build your site around the traditional LAMP stack of Linux, Apache, MySQL, and PHP that most hosts offer. You could set your server up to run alternatives like Nginx, SQLite, and Python if you wanted. The operating system is a bit more fixed but I was given a choice between several popular Linux distros and I could use windows if I was willing to pay more.
The downside to all this freedom is that a VPS requires a lot more work to set up and maintain. If you don't have much experience working with Linux it's going to take a while to teach yourself everything before you can get up and running with a website. On the other hand, setting up your own server is a great way to learn UNIX. Which is one of the reasons why I am rolling my own VPS server.