A is for Aphasia virus. DS9 was struck by one in 2369.
B is for Ba'ltmasor Syndrome. A Klingon malady.
C is for Clarke's Disease. It killed Henry Archer.
D is for Denebian Fever.
E is for Epidural Hematoma. Chekov had one.
F is for Freighter blight. Scourge of Malon officers.
G is for Gorch.
H is for Hyperthyroidism. Artificially induced by Dominion genetic engineering.
I is for Ivonian flu.
J is for Jean Luc Picard who suffered from Irumodic Syndrome later in life.
K is for Kalla-Nohra Syndrome. Caused at Gallitep by inhalation of toxic gas.
L is for the Levodian flu, a mutated strain of which became airborne in the mid-22nd century and infected millions of Klingons, causing their head ridges to disappear and their appearance to become more humanlike.
M is for Melkotian Mumps.
N is for numb tongue.
O is for Orion Pheromonal Fever.
P is for Phage.
Q is for quadrotriticale blight.
R is for Rigellian Kassaba Fever.
S is for Scalosian Scabies.
T is for the Tellurian Plague, one of the most virulent and dangerous epidemics known to 24th century Federation science.
U is for Ulian Flu.
V is for Vulcan Pon Farr. If it can kill you; it's a disease. Probably genetic.
(No "W" diseases in Trek I can think of or find) X is for Xenopolycythemia.
Y is for Yarim Fel Syndrome. It killed Tekeny Ghemor.
Z is for Zanthi Fever.