If you could travel back in time and observe one historical event (as a fly on the wall, you wouldn’t have to participate), what would you choose?
I’d have to go with the assasination of Iulius Caesar.
I’d have to go with the Big Bang.
Since you’ve offered me the chance to watch it, you’ll have to figure out where I can watch from.
Doesn’t Milliways have a sister restaurant there?
I think Hiroshima, 8/6/45 would be interesting.
And there are dozens of great battles throughout history I couldn’t choose from.
Crucifixion of Jesus, if it really happened. I’d want to make sure I could do a substitution if I accidentally chose a fictitious event.
October 31st, 1517, 12:00 noon: Martin Luther nails the Disputation of the Power and Efficacy of Indulgences to the door of the Castle Church in Wittenberg, Germany.
Without a doubt, the lunar landing, first hand.
Luckily for me, since my event is so short and so specifically timed, I don’t have to hang around breathing the lovely body oders emanating from unwashed medieval men. 
You know, I could claim that “oder” is an accepted variant of the word “odor”, but y’all people just don’t take anybody’s word at anything!
I’d probably choose the signing of the Declaration of Independence, since I’ve always wondered exactly what the mood was like at the moment when those guys actually signed the thing.
The meeting between Richard II and the leaders of the Peasant’s Revolt.
What was promised? What concessions were made?
I’d go to the theater festival in Athens in 414 B.C., and see the original casts of OEDIPUS THE KING and LYSISTRATA. How’s that for a double bill?! And Socrates would be in the audience!
Seeing the Beatles in Hamburg c. 1960 (or was it '61? Or both? I forget…).
I’d like to witness the event that killed the dinosaurs. Then not tell anyone what REALLY happened, except in vague descriptions.
Scientist: “Was it a plague?”
Me: “Cold.”
Scientist: “Was it a meteor?”
Me: “Warmer”
Scientist: “Was it climate change?”
Me: “Warmer.”
Hehehe…
As far as I know this one isn’t a mystery. Wat Tyler was killed on the spot by the Mayor of London. Richard II then agreed to the peasants’ demands, but once the danger was over went back on his word and had about 1500 of them executed. So whatever was promised, they didn’t get it.
The weeks leading up to the crucifixion. I think this might answer a lot of questions.
Either that or Raquel Welsh being chased by a dinosaur.
The first-ever performance of Henry V. I would LOVE to know how the audience reacted, how much they really liked Henry, whether they were expecting to see Falstaff or if rumors of his death had leaked out beforehand, which of the surviving texts is closest to what was actually performed, and all that geeky stuff.
King Lear would be a close second.
Even more so the three days after.
Or, you could be the fly on the wall holding that large bottle of “Parfum pour Les Medieval Men Stinky” and spray it on them. 
Tesa
The battles of Marathon (Greeks vs. Persians), the Catalaunian Fields (Huns vs. Romans and Goths), the Horns of Hattin (Saladin’s army vs. Crusaders), Tenochtitlan (Conquistadors and Tlaxcalans vs. Aztecs) or any other great battles would be great to watch, as would great sieges (El Cid’s defence of Valencia?) or defensive battles (Caesar’s defence in Gaul with a few hundred vs. thousands, where Caesar started by driving the horses off a cliff to make his soldiers fight better? Forgot the name).
Witnessing the Viking army sailing into London to deal with Aethelraed Unraed would also be a hoot, as would the start of Cortez’ big trip to Mexico (running off from Cuba after borrowing the governor’s ships before he’d change his mind, then eventually arriving in Mexico, meeting the natives, burning his ships, then telling his men that they will become their own lords of this land under him or die trying). Seeing some of the journeys of Herodotus or exploring ancient Greece, Babylon, Sumeria, Egypt and Meroe would be wonderful too.