Some ideas... some have already been requested
1) Imminent Armageddon - Must win a victory within "X" number of turns before doom
2) Galactic Storm - wipes out/permanently removes resources in planets in a certain quadrant/area/etc.
3) Back to the stone age - all/a specific field of technology is lost and all associated ships/resources/etc. built are lost. The lost technology must be re-discovered
4) Resource shortage - all resources (military,economic,etc) are lost
5) Temporary ownership - a planet that one owns is suddenly given to another race for loan - during these "X" number of turns, the planet cannot be invaded. After the "X" number of turns are up, the planet is returned to the original owner.
6) Galactic Depression - all costs are doubled for "X" number of turns
7) Space Debris Crisis [a.k.a. Kessler Syndrome] - any destroyed ships leave debris that freely moves and can destroy any ships that it runs into. Can be destroyed by other ships.