Owning your own domain gives you so much more freedom on the internet and I would say it is an absolute necessity to ensure success, as it gives you the option to make changes to your site as and when you need to.
By having your own domain you are in control of your site and your business and you will be able to design or make changes to your site so that it stands out in the crowd, makes your site unique and allows you to do the most important task of optimizing your site for the search engines so that your site can appear high up in the search results. You will also be able to project your own personality into the site.
By optimizing your site for the search engines your site will receive targeted traffic which is exactly what is required to generate web income. This basically is also free traffic if you optimize your site yourself and is known as organic traffic. Taking Google as an example, if you do a search the sites that appear on the right hand side of the page are Adwords adverts which are paid adverts. The sites that appear in the main body of the page starting on the left are free and if you have your own domain you can optimize your site so that it appears on the first page of Google. It has also been proven that the first place your eyes look at on a web page is the top left hand part of the page, so ideally that is where you want to position your site in the search results.
With your own domain your advertising options will not be limited, as they are with affiliate urls, as some sites just do not accept them. Also imagine if you were one of a few thousand affiliates belonging to the same program, you would all have the same url. If you had your own domain you could still join a few affiliate programs and then advertise those programs on your own site. Amongst other things, you could create your own splash pages for different programs, add a fly-in, a pop-up, contextual adverts or Google Adsense - your options are not limited.
It makes linking so much easier too, as sometimes to get listed in a high ranked directory you will be asked to place a link-back on your home page, in the form of a text link or image. You could also add a reciprocal linking program to your site. You can so easily place advertising banners on your site, add articles or other items of interest to attract visitors to your site and have them stay on your site longer as well as increase your rankings in the search engines.
Free web tools are a great feature to offer on your site enabling the visitor to check their Link Popularity or Alexa Rating for example. It also enables you to add features to your site that encourage your visitors to return. Add a small piece of script enabling your visitors to bookmark your site. You can offer freebies such as e-books.
Then of course there is the option of adding video and RSS feeds to your site, linking it to your blog as well as all the other technical things available.
You would also be able to add your own email autoresponder campaign that automatically follows-up with your website visitors who subscribe to your Newsletter. So whenever you want to add new products, re-arrange your site layout, change the color scheme or anything you want, you can do it all instantly.
The list of what you could do by having your own domain is limitless, that is why I feel it gives you total freedom on the internet, increases your internet marketing options and generates more web income. 
