Really depends what you are interested in doing, your level of technical skill, and how many sites you're talking about running.
It has been my experience over the last decade of doing this, that most web sites do not and should not be run on their own servers unless they are making enough money consistantly enough to pay for the expense of doing it. A web hosting company, or high volume e-commerce site would be good examples. Running a web server is not something you should be doing on a resedential line. It's possible, but generally not a good idea.
There are a few options.
1. Co-location
Putting your web server in a data center and paying rent. You're looking at 50 to 250 a month for this service depending on where you host, and what your needs are. Problem with colo is that it requires a fair amount of technical skill and you're stuck if anything goes seriously wrong with your machine.
2. Shared web hosting
Very affordable. Hosting plans are all over the board. I pay $10 a month and host 30 sites on one of these plans with no trouble. On the other hand, you could pay up to $100 a month for different levels of service and support with different companies.
3. Buy a t1.
I hear Speakeasy.net has T1 lines starting from $500 a month. Think of having a T1 line like co-locating in your living room. It's a lot more expensive than colo, but offers several major advantages. One big one being that you don't have to worry as much about bandwidth charges and overages. If you have a high volume site and can afford this, it's a good bet. Another advantage is that you can hook any kind of computer up to a T1. With colo, you're almost always (one exception I can think of) limited to Rack mounted servers (those thin looking flat looking ones). So you save there. But you're still paying more for the line, and limited in your support options.
4. Dedicated hosting.
I like dedicated hosting. It offers many of the advantages of colo, without the need to know a lot about the inner workings of your machines. You can find dedicated service ranging from $100 a month, all the way to $1000 a month and beyond.
Again,
You don't need your own web server to host a million web sites. In fact, most of the time, it doesn't make sense (unless you plan to resell service). But maybe your needs are different. The type of service you get should reflect those needs, and your budget. It's all reletive.
Side note:
I can provide links to the services mentioned above if you are interested.
Happy Holidays!