Can I save Roggvir?
When you walk into Solitude for the first time, there is a Nord being executed for helping Jarl Stormcloak escape.
Is it possible to save this man from being executed?
Perhaps more importantly, is it useful to save him? (Or is he scripted to die?)
Solution 1:
Yes and no.
Yes, you can save him, but its not useful in any way or form. He is very weak, and will die in 1 hit. As soon as you start attacking the guards, he will try to run away, causing other imperial guards in the city to take him down with 1 arrow.
If you do manage to kill the 3 guards fast enough, then you can interact with him, but there's no dialog. All he says is "hmm", "huh", "what do you want (insert race)?" etc.
No, even if you killed the guards, the executioner, and the captain, and Roggvir survives, in a few seconds, he will die, even though no one attacked him.
Solution 2:
Looking at the scene Captain Aldis and Ahtar will do whatever they can to kill Roggvir, but Captain Aldis will try to hit Rogvir first when you interrupt the execution. So, you first need to prevent Captain Aldis from killing Roggvir by walking over the ledge in the bottom right of yx's screenshot (this will not trigger the scene, allowing you to interrupt earlier) and simply hitting him, then hit Ahtar afterwards.
Then Roggvir will be able to run away which gives you time to kill both Captain Aldis and Ahtar. Make sure you that you keep both Captain Aldis and Ahtar in place or kill the one that goes for Roggvir. Combine a companion, potions, shouts and other items in your strategy to be more effective.
Contrary to what yx writes, I have not seen imperial guards kill him. Only Captain Aldis and Ahtar where trying to chase and kill him, my companion managed to slow them down while I was following Rogvir and he was kneeling on the stairs where I had to wait for Ahtar to actually come and kill him. This was of course not the best place as I got overwhelmed there, keeping the action near the execution place is the best you can do in order to stay alive. It requires some practice though.
Please note that you will get a 1000 gold bounty on your head for murder, given that he does nothing useful in return it is not worth it to save him from getting executed. In the end, you might even be killing two persons that might be more valuable than the one you are trying to save...