Becoming Thane

After you kill the dragon in the Main Quest Dragon Rising, Jarl Balgruuf the Greater decides to give you the title of Thane of Whiterun, giving you a housecarl (Lydia), and allowing you to purchase property in the city. Guards will also think twice before arresting you if you inform them you are the Thane.

Whiterun isn't the only Hold where you can become Thane. This page is here to help you if you decide to take your lust for power to the other holds in Skyrim.

Whiterun
As stated above, you become Thane of Whiterun during one of the earliest main quests. Simply kill the dragon, discover that you're Dragonborn, and the Jarl will practically trip over himself in his eagerness to make you a Thane.

Morthal
Becoming Thane of Morthal is fairly straightforward. First, you investigate the house that burned down and complete the subsequent quests. The grateful Jarl will tell you that she'd be happy to make you Thane as long as you are "known through her Hold." This translates into helping three different people, all of which can be found in the limited square mileage of Morthal.

Markarth
The politics of Markarth are quite complicated, and thus becoming Thane is as well. The idea is to complete enough quests for both the Jarl and his Steward, driving out the Forsworn from their city and their hills, as well as completing the Civil War Quests. The Jarl will then make you Thane of Markarth and appoint you a housecarl, Argis the Bulwark

Kill Forsworn for the Jarl and his Steward. Help five citizens of Markarth and he'll make you Thane.

Solitude
Talk to Falk Firebeard in the Blue Palace, and he will give you a quest summoning you to investigate lights and sounds coming out of Wolf Skull Cave which is located in the mountains west of Solitude. After completing the quest, talk to Falk again and he will reward you. Sometime soon you will receive a letter from a courier asking you to speak to Falk once more. (It is unknown if you can go talk to Falk immediately after and simply force him to give you the next part of the quest).

Falk will give you another quest. Once this quest is done, you may speak directly to the Jarl herself, and she will thank you and give you one more task.

After you have completed this task go back and talk to the Jarl. She will invite you to be a thane of hers but in order to be a Thane, you must first own property in Solitude. This property can be purchased from Falk for 25000 gold pieces. Once you buy the property, go and talk to her, and she will appoint you to be a Thane of Solitude.

Falkreath
This Hold is as straightforward as Morthal: Obtain a drink for the Jarl, then kill the assigned Bandit Leader. Complete three quests for locals and you're set. This is the standard formula for the smaller Holds (that is, Holds like Morthal, Windhelm, and Falkreath).

- Sell Veggies to the Farmer, Deliver the ashes to the Hall of the Dead, and Retrieve Runil's Journal from Greywater Gorge. - The quest for Runil's Journal pays $1000 gold.

Riften
Connected to the Thieves Guild Quests.

Windhelm
The objectives you need to complete here are as simple as is Morthal. Obtain the Helm for the Jarl, and then help out three people in his Hold, and he'll see fit to make you Thane.

- Dependent on civil war quest

Dawnstar
Thane of Dawestar is obtained by completing the following tasks:

The quest "Waking Nightmare" begun by talking to Erandur in the inn.

Then complete three minor quests A forth quest for the local museum also exists, but if the other three are completed it is not necessary.
 * Give a drink to Karl one of the miners.
 * Sell ore to the iron mine owner Beitild.
 * Fetch Fine Void-Salt for Captain Wayfinder.

Winterhold
Complete all the 'Eye of Magnus' quests and you will be made into the archmage of the college.

-This is different than thane which you can also become by helping the jarl and then helping 3/3 of his people.

Thane:

Retrieve the helm from a shipwreck for the jarl, help three of the people.

-Help the drunk in the tavern by giving him mead