Some statistics: If my count is right, there are 212 stories in total in all 10 SNW volumes, 209 of which were contest winners. There are 51 TOS stories, 51 TNG stories, 27 DS9 stories, 49 VGR stories, 16 ENT stories, 17 Speculations stories, and one "If Klingons Wrote ST" story.
All in all, there were 9 tribble stories, 8 Q stories, and 11 Borg stories (including 2 Borg-origin stories). There were 4 "City on the Edge of Forever" variants/spinoffs and 4 other stories featuring the Guardian. There were 5 stories about characters reacting to Kirk's death (either the apparent one or the real one) and 3 about Kirk having after-death experiences. There were 4 Gary Seven stories, 3 "Piece of the Action" sequels, 3 Kobayashi Maru stories (two about Nog), 3 Captain Proton stories, and 3 Benny Russell stories (counting the Captain Proton story supposedly written by Benny Russell). And I believe there are 5 stories that cross over lead characters from at least three different Trek series, either in succession or in combination (and 3 of those are in the current volume). Still, overall there was a great deal of variety among these and the other stories.
I don't have time, so I'll leave it to someone else to compile statistics about how many authors participated and how many had 2 or 3 stories.