I see that Google and Blogger and maybe other have a customized Google Plus URL.
Google is only beginning to roll out these vanity URLs. Currently, only a few thousand verified and well known people and brands have it, although they will be adding more over time. See this post for (not much) more information.
In the meantime, you should be able to create a redirect from your own website to your profile. (It may be argued that this is a better solution, even.) You can also setup a Google+ Badge to let visitors to your website go to your profile or follow you directly from your site.