My favorite, or in this case most embarrasing se4 moment:
I was playing a game against the AI, and was not meeting much, if any resistance. I was in first place and nothing could stop me from winning. Because I wanted something of a challenge I made the AI a offer it couldn't refuse: I offered to trade all my planets and ships in exchange for one of his planets, and was planning to rebuild my empire from there.
Strangely the AI refused the trade and made a counter proposal, all my planets and ships for an unknown planet. I was suprised but accepted.
Next turn I figured out what had happened, the planet the AI had given me was exterminated by a plague, with no population and thus, no construction possibilities I had lost the game
but it was a lot of fun...