Yes, you probably should.
I am all for DYI projects and it is very easy to setup your own web hosting server. In fact, if you are only hosting a simple website for one business, the computer you are using right now probably has the specifications to run a basic web server.
However, as your audience grows and more people access your site the computer may not be able to handle the work load anymore and neither might your internet connection.
If you are interested in hosting your own web server I highly recommend you read this guide on Linux and LAMP. All the software you need to run a simple web server is open source and free and a lot of fun to play and learn about.
Benefits of a Web Hosting Company
The benefits of using a web hosting company over doing it yourself far outweighs.
First, lets start of with the upfront prices. If your web site goes wide and gets a lot of views, you are going to need the infrastructure behind it to accommodate the load. This includes a power web server computer and a lightning fast internet connection. Both these are expensive and complicated.
Next, looking after web servers is a full time job. Not only do you need to administer it and make modifications. You also need to keep it updated, patched and protected, all while keeping your website on;line so people can access it.
This involves a vast knowledge and experience and the ability to learn on the fly and work under pressure in the face of fighting attacks, when all you want to do is run your business.
Plus, the upfront expenses can be in the thousands of dollars.
Where as, if you use a web hosting company with shared hosting you can get all that including someone who looks after it full time for less than $100 a month!
Cons of a Web Hosting Company
I have only ever had one problem with a web hosting company.
The only real problem is you are at the mercy of the hosting company. There is always a chance they like any business and stop operating .
Also, if someone does something on your website that violates the terms of your hosting service, the web host can ban your website and account instantly.
Most of us will not be looking to do anything bad with our web sites. But if your site is a forum for example which relies on pother people populating it with data and posts, if they post something against the terms of service for that host you could loose your site.