Which is correct?
The newspaper described the success of people like Bob and Joe.
The newspaper described the successes of people like Bob and Joe.
Both sentences are correct, since success can be used as a countable or uncountable noun.
Both are correct, but have slightly different meanings.
"Describing the success" of someone has a more general tone. For instance, the article might discuss Bob's overall career - e.g. "he rose to the top of his company and turned it into the worldwide market leader it is today."
"Describing the successes" of someone implies a discussion of each particular triumph. For instance, the article might discuss particular events in Bob's career - e.g. "his high-quality tender won his company the crucial widget contract with GloboCorp. He then was selected as team leader despite being the youngest on his team."
Both are correct in their own sense.
Success can be pronounced as the dual meaning to target one or more than one person i.e., countable as mentioned above.