I’d learn the Trojan for “There’s Greeks in that horse!”.
I’d screw with it a little more literally, but I can’t decide with who.
Jokes Skald! Jokes! I like you 
Or securing the plans (and the cigars) before he got there.
Or convincing Ewell that he should take the high ground at Gettysburg.
Or convince Jefferson Davis should leave Johnston in command until the election of 1864 was over.
I would convince MacArthur to write a clause into the Japanese constitution that prohibits censorship in any form.
The bad news is that I have pressed the “release werewolves” button.
The good news is that due to a wiring mistake, I released the comfortbots instead.
The Greeks were the bad guys in that conflict. I’m not sure why you think I’m going to be in favor of interfering with them.
Hey Skald, thanks for the lift!
You can see me in this picture now:
I’m over near the righthand side.
Vaccinate the population of The New World in 1490. I’ll need to borrow some pestilence-bots and retrofit them.
I want to give the natives a sporting chance this time around.
I’d go back to Sagres Point in Portugal around 1420 and give Prince Henry a quality world atlas.
I could probably convince Harold Hardrada to wait for his whole army to land and put on their armor before marching against Harold the Saxon.* That would play some havoc with history.
I would give a bunch of money to real-life mad scientist Nikola Tesla. He was almost always underfunded, from what I recall. Imagine what the world would look like if he actually produced large numbers of earthquake machines, remote controlled death-submarines and hand-held lightning cannons!
*I would march with them myself, but Skald is being a party pooper with the no killing thing.
This sin’t quite in keeping with the OP, but I’ve always wondered what would have happened if Columbus hadn’t returned from his first voyage to the New World. How long would it have taken for someone else to try sailing that far west? And what would happen if they didn’t return either? How many unreturned voyages would it take before people decided that those ships really were sailing off the edge of the world? How long would it take the Europeans to just give up? And if the Europeans were artificially prevented from making contact with the Americas, which would happen first–the Americans sail east and make contact with Europe, the Chinese sail east and make contact with the Americas, or the Americans sail west and make contact with the Chinese?
An infinite amount? Since it was fairly well established science at the time that the earth was a sphere. The only question was how big of a sphere it was. I don’t think anyone believed there was even a small chance you could just sail right off the edge of the world.
I thought that the reason they speak Portuguese in Brazil is that a Portuguese ship intending to sail around Africa swung a little too wide to the west.
Convince Lincoln that the play wasn’t worth going to see.
Nope, see Papal Line of Demarcation
Can I go get a sauropod and drop it off in Loch Ness in 1910? How about finding out who Jack the Ripper was but then implicating Anton Checkov, mostly because I hate The Cherry Orchard and I wonder if they would still name the Star Trek character after him is they thought he was crazed killer.
I’ll have you know I can kill people in very creative ways. 
However, given that killing is forbidden I will just have to indirectly cause death - by screwing with the discovery of penicillin.
Sure, it would probably be discovered later anyway, but who knows what flow on consequences the delay could have.
Although, what happens to me afterwards - am I stuck in the past, do I cease to exist ??
Priorities, Skald! Selfish needs first, then causing misery for others.
In fact, chances are pretty small anyone else would have tried it for a long time if Columbus failed to return. Columbus was the only dude dumb enough to believe the world was small enough that you could reach Asia by sailing west before you ran out of food and fresh water. Everyone else was convinced the earth was twice as big as he thought AND THEY WERE RIGHT! (those ancient Greek geometers knew their stuff). Running into the Americas has to be the biggest piece of dumb luck ever to rescue a doomed enterprise.
Anyway. For my project I’ll be taking an accurate map of “Vineland” back to Bjarni Grimolfsson, with pointers to maybe try a little more southerly and warmer for his makeshift colony. Dunno what the results of that might be, but it would sure be interesting.
If Simon Magus really did exist, and really did try to fly, introduce him to a balloon filled with helium.
I would introduce movable type and gunpowder to Archimedes. We would have back-up copies of the Library of Alexandria. Imagine having integral calculus and firearms available to the Romans. The rest of the world wouldn’t stand a chance.
Go back to the days of the nastier popes, set up hidden speakers in the Sistine Chapel and play the “Dies Irae” from the Verdi Requiem at full volume at a key moment, just to scare the crap out of them. Maybe throw in some lighting, projection and smoke effects too. Haven’t decided which corrupt pope to torment yet, but it’d be fun to see if I could scare one straight.