Regardless of the specifics of your domain, the Kano model is a good theoretical framework to start with when looking to delight users. In its simplified form, it divides features into three categories:
These features are required for any level of satisfaction but will never delight or increase satisfaction - at their worst they are dissatisfaction drivers and at their best they are only neutral.
These features drive value when done well and detract value when missing or done poorly - these typically make up the bulk of a product’s feature list and serve as the basis for marketable value
These features drive excitement and delight when present but cause no dissatisfaction when missing - since they are not expected they are often considered remarkable
A given feature will likely span all three categories at some point in its lifecycle. Beginning as an excitement generator, it will become a performance attribute as users grow accustomed to it, and eventually will come to be completely expected and no longer contribute to increased satisfaction.
The bad news is that this natural process is sped up for loyal users because of the frequency they interact with your application. The good news is that the bulk of your work on basic expectations and performance attributes is already done (for now!), so you can focus your time on the little things that deliver delight.
One clear way to do this is to focus on seemingly small UI details that often go overlooked but can completely change an experience. Apple is definitely a leader in this space (here’s an example) but you can find examples in many places. The fantastic tumblr called Little Big Details is a good source of inspiration for these types of design choices. Since most competitors, and other websites in general, don’t focus explicitly on these small interaction details, they can remain excitement generators longer than other features can.