Maybe not a long term butterfly effect, but Philadelphia thought they were getting Ray Bourque at the 2000 deadline. Allegedly Boston GM Harry Sinden disliked the idea of Bourque chasing a Cup on a rival Eastern Conference team. Bourque wanted to be moved to Philadelphia so he could still be somewhat close to his family. Philadelphia played in Boston a couple days before the eventual trade went down and Bourque thought there was a chance he was going to join the Flyers on the flight back.
But eventually Boston gave Colorado GM Pierre Lacroix permission to talk to Bourque and he accepted them as a destination.
I think the Philadelphia offer was Daymond Langkow (in the midst of a breakout season), a 1st round pick, plus a choice of Mark Eaton (stay at home D) or Andy Delmore (offensive minded D who struggled in his own end).
Boston, who also included Dave Andreychuk, took Colorado's offer of Brian Rolston (year removed from a breakout year but was struggling badly that season), prospects Sami Pahlsson / Martin Grenier, and a 1st round pick.
Because of the timing, Philadelphia wasn't able to add anybody on the back end for the playoff run. They were a game away from the SCF. Bourque could have put them over the top.
And then I don't know if Colorado wins the 2001 Cup without Bourque.
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Maybe a smaller one. I can't seem to find definite proof that it happened, but I vaguely recall that the Kings/Sharks had a 2007 deadline deal in place to send Rob Blake for Evgeni Nabokov. At the time, Vesa Toskala had taken over as the starting goalie so Nabokov was viewed as expendable. That was the season where LA used five goalies (Garon/Burke/Cloutier/Brust/Fukufuji).
As I remember it, Blake used his NTC to block the deal. He had just signed back in LA and wasn't ready to leave after several months.
Nabokov would win back the starting job and Toskala would be the one traded instead at the ensuing draft which led to San Jose drafting Logan Couture. Blake would end up signing in San Jose in the summer of 2008.
But imagine a world where the Sharks proceeded with Toskala and don't have the picks to draft Couture. Meanwhile in LA, does Nabokov improve them enough in 2007-08 that they aren't in a position to draft Drew Doughty?