I thought it might be nice to have a thread where we can have up to date info on the Mega Events that are in the game (both base and DLC). I did something similar for Steam Achievements and it seemed to go over well.
As time goes by, I will periodically keep this updated.
I'll break this in to two sections: Base and Mega Events DLC. If anything else Mega Event-y comes from a different avenue, I'll note that as well.
Base Game (as of 1.3 opt-in 2) 
- Anomalies: A lot of anomalies are spawned on the map.
- Breakthrough: A random technology is given to all factions.
- Distant Resources: Elerium and Antimatter are spawned on the map.
- Gold Rush: A smaller amount of anomalies are spawned on the map. (Triggers more often and earlier than Anomalies Mega Event)
- Land Rush: Several Dead Worlds are converted into Habitable Planets. (Class Range will be edited in/added when known)
- Paradise Worlds: Several Dead Worlds are converted into Class 25 planets. (Triggers later and is rarer than Land Rush)
- Pirate Colony: A Dead World is converted to a Class 6 planet and assigned as the Civ Capital for the Space Pirates faction.
- Relics: Precursor Relics are spawned on the map.
- Resource Glut: Random number of Asteroids, Dead Worlds and Gas Giants are converted into Durantium, Thulium, and Promethion respectively.
- Wormholes: Wormholes are spawned on the map.
Mega Events DLC (as of 1.3 opt-in 2) 
- Assassination: The player is plunged into war with a random faction.
- Bank Robbery: The player is offered a set of choices involving Credits and Diplomacy.
- Brains Not Brawn: A new Minor Race, the BRAINY'AK, specializing in technology but with almost no military is discovered.
- Dreadlords: The Dreadlords have returned! OMG!1!. (The Dreadlords spawn on a random planet)
- Helping Hand: A choice between halving all Manufacturing for a set amount of time and receiving Research Points in return is offered to the player. Rewards and penalties vary.
- Life Support: A choice over sharing a breakthrough that doubles the range of all ships with other factions is offered.
- Ludicrious Speed: A choice involving boosting the speed of ships of only your own faction or of all factions is offered.
- Peacekeepers: The Peacekeepers arrive, attacking any and all factions that are currently at war.
- Pirate Outbreak: A new faction of pirates, tougher than normal, are spawned on the map.
- Renaissance: A choice involving research being increased to all players or a set amount of tech points to the player alone is given.
- Space Monsters: The Space Monster faction is spawned on the map.
- The Artifact: The faction in the game which is currently the weakest gets a cumulative increase to their Production Points every turn until the end of the game or they are eliminated.
- Wish Upon a Relic: A choice involving greatly increased Research and Manufacturing for the next 25 turns is given.
I haven't given full details for the more involved ones. Perhaps I will provide a full breakdown of what each Mega Event does if people wish.
I am mostly going off the XML details here. I might adjust the above list as needed as actual game play comes in.