While WordPress is doing a great job of simplifying the job of building a website, there is one thing which WordPress can’t do. Being a free and open source platform, you can’t expect it to offer you a unique website, with unique look or feature. Even if we ignore the free themes, the theme you purchase can be purchased by others as well. The same goes for plug-ins and add-ons as well.
There thrives the market of unique website development. There are agencies which offer custom website development as a service and what they do, while expensive, gives you a feeling of exclusivity. For example, you can ask them to build you a feature or a tweak as per your vision. In fact, you can draw the whole website on a paper and ask them to build that. As they build the website from scratch, you can expect them to deliver that.
However, this means a lot of work and expect the charges to be higher than the WordPress web development. The agency will sit with you and understand the unique features you need, the animation or eye-candy you require and they will also ask you to draw a wireframe for them, if you have one in mind. Once done, they will come up with the first version and then you are free to find faults or deviations from your idea. They will go back and redo those parts. This reiteration will take place till you are completely satisfied with your website.