Skyrim - Main Quest 1 - Unbound

The game begins with you in Imperial custody, alongside Jarl Ulfric Stormcloak, Ralof, and a horse thief named Lokir. You were taken prisoner after running into an Imperial Army ambush while crossing the border to Skyrim. The prisoner caravan you are part of is destined for the small Empire stronghold of Helgen. After you get off the cart, the guards begin calling out names, looking for members of the Stormcloaks. Eventually, you are ordered by an Imperial soldier named Hadvar to identify yourself, which will lead to a prompt to create your character. Despite your lack of involvement with the Stormcloaks, the captain of the guard orders you to be executed. A Priestess of Arkay will start saying a prayer, but as soon as she mentions the eight divines a stormcloak will interrupt her, and the executions begin. Not long after the executions start, they call you forward. Following the direction given to you by the guards, you lie down on the execution block. 
Right before the executioner can bring his halberd down on your neck, the dragon Alduin arrives and disrupts the execution. With the execution stopped and the guard in chaos, you take the opportunity to escape custody, and at this point the cinematic ends and you gain control of your character's movement with Ralof desperately yelling at you to get up. Run with Ralof towards the nearby tower, in which you will find several Stormcloak soldiers and Ulfric Stormcloak, who also escaped in the panic. Climb the stairs to where a Stormcloak Soldier is trying to move some rubble blocking access to the rest of the tower. Alduin will blast a hole through the wall and use a shout to breathe fire into the tower. Ralof will instruct you to jump out of the tower through the hole into a nearby building, with the promise that he will meet up with you when he can. 
After jumping down and exiting the inn, you will find that Helgen has become heavily damaged in quite a short time, with many buildings ruined and burning. The defending Imperial soldiers are caught up in the battle and are too busy to take any notice of you. Run into the street and you will encounter Hadvar, attempting to rush civilians to safety. One injured Nord, Torolf, unfortunately fails to escape the carnage, and is killed by the dragon's fire breath. His son, Haming will cry"Get up, papa! Get up!" and Hadvar will yell out to the child to get to safety. He'll then tell Gunnar Stone-Eye, "Gunnar, take care of the boy. I have to find General Tullius and join the defense." After Alduin flies away to attack other targets, Hadvar will tell you to follow him if you want to stay alive. He will lead you towards Helgen Keep, a large Imperial fort in the village, passing a number of Imperial Mage soldiers defending Helgen on the way. At the entrance to the Keep, Ralof will catch up with you. At this point you must choose whether you wish to accompany Ralof or Hadvar for the remainder of the quest. 

Note: After entering the Keep, depending on whether you chose to enter with Hadvar or Ralof, the part of the interior map which you emerge in and the initial events that occur will differ slightly.
If you choose Ralof, you will discover the body of a dead Stormcloak, Gunjar, in a circular room immediately after entering the keep. After freeing you from your bindings, Ralof will instruct you to recover the gear on Gunjar's body for your own use. While you equip yourself, Ralof will examine the doors. He will discover one door is locked, and the other can't be opened from the side you're on. Luckily, two Imperial soldiers will come through and open the door secured from the other side. Once they open the door, you will be forced to kill them to recover the key to the other gate from their bodies. Don't forget to loot the barracks they came from.
If you choose Hadvar, you will enter the keep to find yourself in the barracks room where Hadvar will cut your bonds and instruct you to loot the room for some equipment. Once you have acquired some gear from the marked chest, he will open a secret passage and you will follow him down a path to the circular room containing Gunjar's body. Here you will face two hostile Stormcloaks. Once they are defeated, follow Hadvar onward through the opposite door.
From here onward the physical path taken by both Hadvar and Ralof is identical. Only the type of enemies and the accompanying dialogue is different: for Hadvar's path you face Stormcloaks, for Ralof's path you face Imperial Soldiers.
Going through the door onto the now opened-up path, the dragon's activities above will cause the ceiling to fall, diverting you through a door on your left, where you will discover a store room with two Imperial Soldiers/Stormcloaks gathering supplies. After defeating the enemies, Ralof or Hadvar will advise you to go through the barrels for any valuables you may obtain such as potions.
Continuing down, you will arrive at an interrogation room, where a battle between an Imperial torturer, his assistant, and some Stormcloak Soldiers is taking place, prompting you to fight with whichever enemies your escort is not aligned with. If you are with Hadvar, he has a conversation with the torturer, trying to convince him to come; his attempts are futile, however, as only the assistant torturer follows. If you're with Ralof, he has a quick conversation with the surviving Stormcloaks, who will both choose to follow your party. Hadvar/Ralof will then point to a cage with several valuables inside it (including mage gear and a spelltome), offering you several lockpicks, and suggesting you pick the lock to get to the items.
Continue down the corridor past some prison cells which can be unlocked for some minor loot, and through another prison room, and you will eventually enter a natural cave, filled with either Imperial soldiers guarding it for General Tullius, or some lost Stormcloaks. There is an oil spill that can be set alight to damage the enemies on the upper level using the Flames spell.
After killing them, you will find a raised drawbridge obstructing your path. Hadvar or Ralof will lower the bridge and shortly after you cross it, the passage behind you will collapse. After some further exploring, you will discover a Frostbite Spider nest. Once you defeat the spiders, head through a passage leading deeper into the caverns. Next, near an underground stream, you will encounter a resting bear. Ralof/Hadvar will advise you to sneakpast it, but he will give you a bow and some arrows in case you choose to ambush it. Fighting the bear is not too difficult with Hadvar/Ralof helping you. Afterwards, follow Hadvar/Ralof and exit the cave through a crevice in the rock.
Leaving the dungeon, you'll see the dragon flying off into the distance, towards the north, completing the quest. Your companion will recommend that you split up, but you can follow him nonetheless. He will guide you to his home town of Riverwood, showing you both the ominous Bleak Falls Barrowand the Guardian Stones along the way. He will comment differently depending which stone you choose.

The Warrior Stone (Ralof): "Warrior, good! Those stars will guide you to honor and glory."

The Warrior Stone (Hadvar): "Warrior, good! I knew you shouldn't have been on that cart the minute I laid eyes on you."

The Mage Stone: "Mage, eh? Well, to each his own. It's not for me to judge."

The Thief Stone: "Thief, eh? It's never too late to take charge of your own fate, you know."

After arriving in the village, the path differs depending on your follower: Hadvar will take you to his uncle Alvor - the town's smith - while Ralof takes you to his sister, Gerdur, the owner of Riverwood's woodmill. After a lengthy conversation concerning the events at Helgen, Alvor/Gerdur will ask you to warn Jarl Balgruuf the Greater in Whiterun of the dragon (starting the next quest), and will offer to let you stay at their home and offer some gifts of food and potions.