Is there any way to see how many times your character has died?

The question is pretty much in the title. After finally beating Hell with my Witch Doctor, I was interested in knowing if there is a way to look up how many deaths it took to get there.

Not yet, but it may be implemented soon, since they're going to add character profiles to the game:

Our first profiles release will include these two elements:

• A career tab that displays all of your heroes, how far you’ve progressed in the Diablo III campaign, how many foes you’ve slain, the names and playtimes of your fallen Hardcore heroes, and more.

• A heroes tab that shows off your equipment (including dyes, socketed gems, all equipment bonuses, etc.), your attributes and skills, the skills and equipment of your Followers, and more.

Presumably one of those two "more" will be your death count, since a similar counter is already present in WoW character's profile.