George Brinton McClellan
Ambrose Burnside
Joseph Hooker
George Meade
John Parke
This question was asked in March of '17 (3/29/17 to be exact). Hoosier had the perfect answer in my opinion. Here it is.
Wikipedia says there were six: Irvin McDowell, George McClellan, Ambrose Burnside, Joseph Hooker, George Meade, and John Parke.
It could be argued that McDowell shouldn't count, since the army wasn't called the "Army of the Potomac" when he commanded it. It could also be argued that McDowell should count, since the army he commanded did ultimately become the Army of the Potomac.
It could be argued that Parke shouldn't count, since he assumed command only temporarily during periods when Meade was absent, with full understanding that Meade would resume command upon his return. It could also be argued that Parke should count, since the question asked for all generals who ever commanded the Army of the Potomac, so even if the command was temporary, Parke did command the army.
Unless somebody comes up with something really surprising, here's the way I plan to score this question.
Correct answers must include all four of McClellan, Burnside, Hooker, and Meade. Because the questions of whether McDowell and Parke should be included are debatable, I will accept answers that include both McDowell and Parke, McDowell but not Parke, or Parke but not McDowell. I will also accept answers that exclude both of them.
Better words were never said on this question.
It wasn't "The Army of the Potomac" until Little Mac took over, so McClellan is #1. While he was reduced from General-in-chief, he remained the army commander until replaced by Burnside, who was replaced by Hooker, who was replaced by Meade... and Meade had it for the rest of the war.
civilwartalk.com
Edit - Thanks for the kind words.
Interestingly, the person who posted the question in March of 2017 was BrianB - the same person who posted the very similar question this time. However, this time he took care to specify that he wanted five names as a correct answer and that McDowell should not be one of them.
So McClellan, Burnside, Hooker, Meade, and Parke are five names that should count as commanders of the Army of the Potomac.
Unless, of course, somebody recognizes (as some of our players did) that there were both a Union Army of the Potomac and a Confederate Army of the Potomac, which opened up P. G. T. Beauregard and Joseph Johnston as correct answers.
hoosier