The biggest reason has to be that a lot of it is extremely well written and the universe it's created is so rich and detailed.
Another big reason I think it's stuck in people's minds for so many years whereas most shows from the same time have been forgotten or treated as a nostalgia item is Gene Roddenberry's vision. Everything I want to happen to the human race happened. That makes me feel good and makes me want to keep watching. And it inspires me to behave that way in our current, less than ideal times.