Great question – I just did an "exit interview" with a senior UX designer who was consulting for my company and this very topic came up. Some insights from that conversation (and some of my own opinions) are as follows:
An appreciation for good design and art is a key input to the design process. If you can't appreciate good design and art, it hampers your ability to such design. And that's in all mediums – film, music, print, hardware, television.
Empathy is a huge thing, and knowing that you are designing solutions to solve the problems of real people makes the designer focus on making the work more approachable, understandable and usable.
The ability to communicate is also key. If you create a good design and can't explain the details of how it works to the people who have to approve or implement it then that design may never be executed, or it it is may become muddled and diluted.
Listening is also key, and with it the ability to take criticism well. Great designers are their own worse critics, but it is not themselves they are criticizing, it is the work… great designers know that they are NOT the work, and so they are open to having the work openly critiqued. By collaborating with peers, listening to their feedback and responding to it, by testing designs with customers, the good becomes great.
Finally, passion is the "secret sauce" that all great designers have. If you are looking at a UX design job as just something to pay bills and "get by," then you probably will never become a great designer. It's the different between someone who writes classified ad copy and someone who pours their soul into a novel. The ad copy will never be great, but the novel has a much better a chance at being so.