
http://youtu.be/fJlv36uWC8c
[Front-paged. -stabguy]
A collection of additional assassinations in AC1, made possible by back to the future exploit.
Maria
Start this the same way as the original early assassination of Maria.
http://www.youtube.com/watch?v=EaikxWTUYVI
Reinitialize the memory by going through the city entrance in the south of Jerusalem. The game doesn't recognize Maria as a target anymore. Now there is no memory corridor scene, and Maria stays dead. It's probably possible to get an instant kill from this by taking out her health and talking to the bureau leader, but I didn't have enough time to record more.
Sibrand
Start this the same way as the original early assassination of Sibrand.
http://www.youtube.com/watch?v=3Tww7kpXiA8
Reinitialize the memory by going through the city entrance in the north part of Acre (there's also an entrance in the eastern part, but you desynch before getting there from the game thinking you already started the mission). Sibrand usually goes onto the docks and walks back and forth along them just like the guard patrol. He's unresponsive to you, but still reacts to seeing dead bodies (in the original Back to the Future assassination he can detect you and would run back to the ship to get to the guard tower). Now that the game doesn't recognize him as a target there's no memory corridor scene. You can also take out his health for an instant kill, but it isn't very interesting.

http://www.youtube.com/watch?v=Apmob4kOYug
[Front-paged by stabguy]
So it turns out Abul Nuquod can be killed before it should be possible, even though you can't get to him without the memory recording.
Setup
For the basic setup watch the original video.
http://www.youtube.com/watch?v=OHvrRuha1K8
You get in the place by countering a guard through the other side of a wall.
Early Death
After glitching inside the palace the memory starts recording before you reach Abul Nuquod. Walk to the front where you can fall off the roof. There's an invisible barrier that prevents you from going back inside (and in this case also a blue memory wall from being exposed). Walk to the nearest city entrance. You will receive a message that the memory will reinitialize if you leave the city. Going further will refresh the memory and allow you to regain high profile actions. So run back to the palace. Guess who is strolling out the side door? Abul, and maybe one of his bodyguards (I've done this only twice, so I don't know the chances). The game doesn't delete them when you reinitialize the memory, probably because they don't appear until the memory starts recording (actually you can see the bodyguards on the balcony from outside the front door, so it's probably based on distance until the memory starts recording). The palace is empty, and there is no target on the map. Even after killing Abul Nuquod you still have to start the mission again.

http://www.youtube.com/watch?v=OHvrRuha1K8
[Promoted to front page. -stabguy]
Getting inside the merchant king's palace just prior to the cutscene (non-story) is something I have wanted to do in a while. Here's the setup.
Infiltration
You need a vigilante for this. Luckily there's a group of them not far away from the palace. You would first want to kill the guards in between where you want to lead the vigilante. Have a guard fight you to lead the vigilante. This could take a while since most of the time is spent watching the guard struggle with him. But then the guard pushes him away and comes again after you. This is how you lead the vigilante. Make sure the guard doesn't get too far from him or the vigilante gives up and goes back to the others. Lead them to the door of the palace that Abul Nuquod exits out of. You will encounter a group of guards. Kill all but three guards uncluding the one used for the vigilante (this doesn't seem to work if there are more than three guards). Now here's how you get into the palace. If you jump on the platform by the wall of the door the guards will think you are on the other side of the wall and go there. It is a little common in the AC games for guards to think you are somewhere else, especially if it's by a wall. Getting guards to go after you by jumping while crouching is known as the Pathfinding Charm, discovered by IanXO4.
http://www.youtube.com/watch?v=PRdq6ioX8NE
This is where the vigilante comes in. You need to be locked onto a guard so that you are in battle mode and can counter kill your way in the palace. Jump only when the guard and vigilante are struggling so you don't have the guard also trying to go in the palace.
Exploring the Palace
After you get in stay close to the wall to avoid the memory starting. Take the path shown in the video. Notice how the rooftop archers are all gone. Now for Abul Nuquod. Unfortunately you can't get to him without the memory starting. In fact he and his bodyguards don't even appear until the memory starts. So just drop by and say hello to them before starting the scene. So infiltrating the palace doesn't have much use besides saying it's possible.
I've gotten out of the palace by dropping from the roof, gone a far distance away, and come back. From the front door I can see the bodyguards are no longer on the balcony, and possibly also Abul Nuquod, but with no way to get inside it's unclear what has changed.

http://www.youtube.com/watch?v=peU2IVE4Ngs
[From the forums - stabguy]
Here are some assassinations I did on Abu'l Nuquod the merchant king.

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The Turkey Shoot: The goal in these assassinations is to immobilize the target so that you can easily stab him/her with the hidden blade. Of course, the developers never intended such assassinations to be possible, so you have to rely on several exploits in order to pull off these types of assassinations.
Here are video walkthroughs for the assassinations shown in "The Turkey Shoot".

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Here are some extremes of hiding in plain sight.
William: After William is done lecturing his men, he goes to his desk to study a map. You can climb down behind William and blend right next to him. If you bump into the table, William will notice you, so you need to be careful as you approach the table. In this video, I line up Altair's shoes with William's shoes to ensure that Altair doesn't bump the table.

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Version 2.0 contains updated blitzes of Tamir, Abu'l, Majd, Jubair, Maria, Robert and Al Mualim.
Blitz assassinations of all the main targets. The concept of this style is to assassinate as quickly as possible, while remaining Anonymous before the kill on certain targets: Tamir, Garnier de Naplouse, Abu'l Nuqoud, Majd Addin, William de Montferrat, Jubair Al Hakim and Sibrand.

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Frequently Asked Question: I'm on Memory Block 4 and there's nothing left to do on my map. What now?