The Captain Could Have Died a Borg: In the famous final episode of Season 3, the Captain had been assimilated by the Borg and the writers were prepared to kill him off in the following episode. This was because Patrick Stewart’s contract had ended and they were not sure if a new agreement could be made
The Admiral Could Have Been the Captain! Edward James Olmos (Admiral Adama on Battlestar Galactica) was offered the role of Picard. He turned it down because he wasn’t interested in working in television at the time.
Also, a co-producer/writer on Star Trek The Next Generation, Ronald D. Moore, eventually went on to become the Executive Producer as well as a writer on Battlestar Galactica.