One of my favorite things about it is that the characters are all interesting. They all have obvious wishes and goals. The main character is trying to rule the world (sort of) by being a supervillain. The love interest is a selfless person that wants to help people that can't help themselves, which is an interesting dynamic for obvious reasons.
Another great thing that this show accomplishes is that since it is so short, they worked a lot of things into every scene. Many songs have overlapping lyrics, which is the easiest and most obvious example. It's impossible to listen and compute to both of the contrasting lines of dialogue, so its easier to just watch it a second time and pay attention to the other side. Sometimes, there are actually three people singing at once. This could easily come off as overwhelming, since one wouldn't know where to focus, but I think that it does a great job telling you what's important while giving people that have experienced it before 'added features' as to what they missed the time before. A second example to this is that a lot of stuff happens in the background of scenes that doesn't call attention to itself, but adds to the characters and the plot.
All things considered, Dr. Horrible's Sing-Along Blog is something I think everybody should experience. I may say that a lot, but it could usually be something of a hyperbole. When I say Fullmetal Alchemist: Brotherhood is one of the best animes of all time, that doesn't mean everybody should see it. Some people don't like anime, and it would be wrong of me to judge them for that. I'm not going to say everybody should see it, because some people wouldn't like it.
No, I'm not trying to imply that every person in the universe will like Dr. Horrible. But it's a great example of how to do things right, most specifically how to layer everything and tie it together to enrich every aspect of what the audience is experiencing. It perfectly encapsulates the idea of blending the familiar with the original, in that the story premise and arc are almost ordinary (even predictable if you're attuned to story telling), but the characters and their specific goals are relatively unique.
Plus, this isn't even an hour long. It won't really take any time out of your day to watch it.