I know of the obvious disadvantages (when you die, you're dead), but what are some reasons to create a hardcore character in Diablo 3 besides the increased challenge?
The whole point is the increased challenge. And along with that, the associated bragging rights that come with various Hardcore Mode achievements. Hardcore Mode also provides a variety of ways to show off how hardcore you are, such as new banner sigils, a separate ranking ladder, and the name of your hardcore character appears in red, so everyone can see how badass you are.
It's an alternate style of play that was extremely popular in earlier Diablo games. It encourages a very different, much more conservative, playstyle, and by having 'skin in the game' so to speak, the sense of risk, and thus, the (emotional) rewards of victory are substantially heightened.
There is a very different play style in hardcore which may make the game more enjoyable to play. In soft core mode players have no fear of death and can choose to build full damage and no defense. You might play games with your friends and die over and over again while you desperately farm act 3 inferno. In hardcore you have to play at a safer pace. Making sure your built defensively enough to live through everything.
Diablo 3 Hardcore characters bring the following benefits to the table:
Your name is displayed in a different color from the rest of the players. (Red)
You are ranked separately from other players. Hardcore players compete with hardcore players in the rank ladder.
You can only form teams with other Hardcore players.
Playing a Hardcore character will make you plan ahead more and play much more carefully as you only have one shot. Once you die, you are gone for good. (Note that you can still chat with other people when you die as a Hardcore character)
As other people have mentioned, the main difference between normal and hardcore mode are the challenges, special achievements, and things to show off how awesome you are.
That being said, for actual advantages, the main thing is that there will be no Real Money Auction House, so only skilled players will be able to survive. Thus, once you get past normal, you can be sure that most players will be skilled and you will not run into players who just bought their way to power.