So far in the series Tyrion Lannister has been a prisoner to almost all of the Great Houses (and some minor ones as well. I thought it would be fun to take a brief look at it.

If interested: Dungeons & Prison of Ice & Fire & Highborn Prisoners of Ice and Fire

Main Prison #1 (The Sky Cells of the Eyrie)

Prisoner of: Houses Tully, Stark, Arryn

Catelyn uses the power of her father's name (Tully) in order to take Tyrion captive at the Inn at the Crossroads:

“The red stallion was ever a welcome sight in Riverrun,” she said to the trio by the fire. “My father counts Jonos Bracken among his oldest and most loyal bannermen.”

The three men-at-arms exchanged uncertain looks. “Our lord is honored by his trust,” one of them said hesitantly.

“I envy your father all these fine friends,” Lannister quipped, “but I do not quite see the purpose of this, Lady Stark.” -AGOT, Catelyn V

Ned Stark claims that Tyrion was taken at his command (Stark):

"It would seem he has met some trouble on the road. My lord father is quite vexed. You would not perchance have any notion of who might have wished my brother ill, would you?"

"Your brother has been taken at my command, to answer for his crimes," Ned Stark said. -AGOT, Eddard IX

Sweetrobin/Lysa then sit in judgement of Tyrion in the Vale (Arryn):

"The bad little man," Lord Robert said, giggling. "Mother, can I make him fly? I want to see him fly." -AGOT, Catelyn VII

If interested: The Blue is Calling: The Identity of the Sky Cell Jumper

Main Prison #2 (The Black Cells in King's Landing)

Prisoner of: House Baratheon, Lannister, Tyrell (kind of Martell too)

Note: Tyrion isn't in the Black Cells until after the Trial by Combat

Tyrion is accused of killing Joffrey (Baratheon), but before he declares trial by battle, he is on trial:

Tyrion turned from the window. "Who is to judge me?"

"Justice belongs to the throne. The king is dead, but your father remains Hand. Since it is his own son who stands accused and his grandson who was the victim, he has asked Lord Tyrell and Prince Oberyn to sit in judgment with him." -ASOS, Tyrion IX

If interested: The Tunnels in the Red Keep

Upcoming ??

Following Patterns: Tyrion's Third Trial by Combat

Tyrion has yet to be a prisoner of the Greyjoys, Martells (kind of) and officially Targaryen. We know that Tyrion and Dany's paths will intersect in TWoW (but they will spend most of the book apart).

If interested: Tyrion's Path: Jon then Young Griff then Dany & Wroth of the Dragon: Tyrion's Provocations to Jon/Young Griff/Dany

"I dreamed about the queen," he said. "I was on my knees before her, swearing my allegiance, but she mistook me for my brother, Jaime, and fed me to her dragons." -ADWD, Tyrion II

• Greyjoys

Tyrion is currently a prisoner/sworn member of the Second Sons, but he could encounter Victarion/the Ironborn after the Battle of Fire. Who knows what will happen with the horn, power vacuum, etc.

• Casterly Rock

Not necessarily as a prisoner but it is often theorized that Tyrion will use the drains of Casterly Rock in order to take the castle.

Minor Houses/Others

Throughout the series it can be argued that Tyrion is also a prisoner/hostage of the following:

• The Vale Mountain Clans (if interested: The Vale Mountain Clans in TWoW)
• The Young Griff Plot (this probably could have its own section, but Tyrion not only "works" aboard the Shy Maid, but also gives the Golden Company/Young Griff some potentially vital info)
• Jorah Mormont
• Yezzan zo Qazzaz (The Yellow Whale of the Slaver Alliance)
• The Second Sons & Brown Ben Plumm

If interested: A (somewhat) recent post on GRRM's progress with writing Tyrion in TWoW

TLDR: Due to some good luck and wit aka (serious plot armor), Tyrion has managed to become/unbecome a prisoner of just about everyone in Westeros/Essos. The only great house he likely never becomes prisoner of is Greyjoy (although I'd love to see Tyrion as a Euron's prisoner on the Silence).