Every year, there are hundreds, maybe thousands, of trade rumors that are spoken of for a few hours and then quietly put aside and never heard of again. There are always going to be players that many expect to be trade, but it never happens.
I have found eight rumored trades that didn't go down over the last 10 years that would have changed the game of baseball that we know of now. The blockbuster status may have been from the star power of the players in the trade at the current time, or because of the star factor that some of the players had after the rumors ended up not coming through. Some will be from right before the trading deadline, while others will be during the offseason.
Editor's Note: If you have some more to add, please let me know if the comments. I did a lot of research, but I'm sure I missed more than a handful (probably a good many). I'll add some of your suggestions, thanks!