I love how Straight Dopers can casually and rationally discuss anything, up to and including the annihilation of life on Earth. 
Regarding the Black Death: “A third of Europe” isn’t actually high at all; general estimates put it right about there. Some estimates for the total death toll from the various forms of plague (bubonic, pneumonic, etc.) range up to half, but then you have to decide how you define Europe, where you draw the borders and how you calculate the population. In any event, in terms of total world population, the toll isn’t that high, because you leave out the Americas. The Black Death (known at the time as the “blue sickness,” FWIW) swept through Asia prior to its arrival in Europe, but records outside of China are pretty spotty.
The Great Influenza Pandemic around World War I is estimated to have killed between 17 and 22 million people, worldwide. Given the population of the time, that’s still the winner for deadly disease outbreaks in known history. AIDS is approaching that total death toll, particularly in Africa, but the higher total population worldwide means it constitutes a lower percentage.
Possible disease threats in the future? There’s always the possibility another strain of influenza could turn up, and chew a wide swath. Also, tuberculosis could be a big problem; lots of multiply-resistent varieties have been turning up, including some that respond to no, repeat, no antibiotics. In other words, if your body doesn’t fight it off on its own, it kills you. Not good, obviously, and TB isn’t the only infectious agent for which multiple resistance is rapidly increasing.
You also can’t discount the possible re-release of smallpox. After its eradication in 1977 (IIRC), samples were retained only in two secure locations in the U.S. and Russia, ostensibly for research purposes; but the Russian military is widely known to be experimenting with smallpox as a bioweapon. (Read Biohazard by Ken Alibek if you want nightmares.)
If a disease takes us out, it won’t be something horrifying like Ebola; that would burn too quickly through the infected population to be passed on to others. Rather, it’ll be something innocuous we think isn’t a problem, like TB or streptococcus.
(Can you tell my wife’s an epidemiologist?)