The benefit of being Thane

In general, getting the title thane bestowed upon you follows a set strategy:

1. Do an introductory quest-line that winds up getting you noticed by the Jarl of the hold.
2. Complete a number of miscellaneous objectives within the hold (5 if a house is available, 3 otherwise)
3. Purchase a house in the hold's capital (if available)

The Eastmarch (Windhelm)

1. Capture Whiterun and Falkreath (if siding with the Stormcloaks) or capture Windhelm and complete "Kill the Bandit Leader" (if siding with the Imperials) to get into the Jarl's good graces
2. Complete 5 miscellaneous objectives within the hold
3. Purchase Hjerim, the house in Windhelm

Falkreath

1. Complete "Rare Gifts" (if given) and "Kill the Bandit Leader" to get into the Jarl's good graces
2. Complete 3 miscellaneous objectives within the hold

Haafingar (Solitude)

1. Complete "The Wolf Queen Awakened" (possibly optional) and "Elisif's Tribute", which gets you into the Jarl's good graces
2. Complete 5 miscellaneous objectives within the hold
3. Purchase Proudspire Manor, the house in Solitude

Hjaalmarch (Morthal)

1. Complete "Laid to Rest" to get into the Jarl's good graces
2. Complete 5 miscellaneous objectives within the hold

The Pale (Dawnstar)

1. Complete "Waking Nightmare" to get into the Jarl's good graces
2. Complete 3 miscellaneous objectives within the hold

The Reach (Markarth)

1. Complete "Dungeon Delving" (different from the Winterhold quest of the same name) to get into the Jarl's good graces
2. Complete 5 miscellanous objectives within the hold
3. Purchase Vlindrel Hall, the house in Markarth

The Rift (Riften)

My complete walkthrough for this is contained in another answer about how to get the house in Riften, but since that's the final requirement for obtaining the title, it's exactly the same. In short:

1. Handle Riften's drug problem by completing the quest chain that starts with Wujeeta
2. Complete 5 miscellaneous objectives in the Riften (can overlap with step 1)
3. Purchase Honeyside, the house in Riften

Whiterun

You've already mentioned how to become thane here, but for the sake of completeness:

1. Travel to Whiterun as part of the main questline
2. Complete the main questline up to and including "Dragon Rising"

Winterhold

1. Complete "Dungeon Delving" (different from the Reach quest of the same name) to get into the Jarl's good graces
2. Complete 3 miscellaneous objectives within the hold

Console command: setstage favor250 20

favor250 is the quest for becoming thane of Markarth

stage 20 is when you have bought a house and done 5/5 objectives.

After becoming thane by talking to the Jarl, you can then talk to his steward, and he will finally sell you a house, for some stupid reason.