update - references added:
Kidney issues http://www.kidney.org/news/KidneyCare/spring10/DietSoda.cfm
Dental issues http://www.wda.org/your-oral-health/sip-all-day
Vascular issues: http://www.miami.edu/index.php/news/releases/study_finds_pos...
Too much milk can give you kidney stones. Too much fruit juice gives you cavities. Too much coffee stains your teeth and gives you, what was it, high blood pressure? On and on.
Of course, too much coffee or tea will kill you the same way.
If anything you're more likely to get messed up from the diuretic effects.
I'm drinking my second Diet Coke (with Splenda®) of the day right now. I find it to be a nice way to get a continual, low-dose of caffeine. More importantly, the flavor and fizz is very refreshing and has good mouth-feel.
Not everything "good" is measured by some objective health metric. And the "bad" about Diet Coke likely pales in comparison to the countless other "bad" factors in people's lives.