Just based on the films, now that his dad Laufey is dead. He has a good claim to rule Jotunheim.
So what he was abandoned for being a runt and hes way short in comparison to the other Jotuns, he still has a claim to the throne, the exiled prince come back to take his throne and become king? Its so Targaryen!

Why did he not try to do this? hes a highly intelligent, charismatic and skilled in all the kingly ways. He knows how to lead and he knows how to make war and create peace, he was on Asgard, Thors understudy essentially. If Thor died Loki stepped in so he had to know all the lines of the play. He got all the same education as Thor precisely for this so its not like hes ill-equipped.

He may not have even had to go through with the whole scheme in the first movie after he found out his true ancestry. He could have marched on Jotunheim and gathered a following and gone to his father and taken steps(schemed most likely) to be legitimized in the Jotun court.(Laufey probably wouldnt welcome him warmly and just admit the past so freely) all that "hey remember me? your son you left out to die? im Baaaaaack ^-^(yeah Lok would have to pull some strings)

Perhaps he could kill Laufey at the right moment on his own turf and after claiming it for his own.

Sure he was the shame of the royal family due to his size but he more than makes up for it. Hed be the Napoleon Bonaparte of the Jotuns. They would follow a short guy if the short guys Loki. Hes fucking Loki! He'd Game of thrones the shit out of that place!

Why he so hung up on Asgard? or stupid earth humans for that matter?

Im sure die hard fans of the comic who know every plotline in every universe will say "He already tried that in issue blah blah blah" and if noone says that because it never happened.....WTF! The good claim, the birthright, all the skills needed plus his overall charm. HE'D HAVE PULLED IT OFF!

Why he always schemeing in the wrong place? Leave earth alone, leave Asgard to Thor and take Jotunheim!

He wants to be a king and run shit? theres a whole realm right there ripe for the taking! and he doesent need dragons either.

In the films, that was Odin's plan: Thor would become King of Asgard, Loki King of Jotunheim, breaking the uneasy truce that had held the two world's for so long in favor of true peace, brotherhood.

What he didn't take into account, however, was Loki's self-loathing at finding out his true identity. Loki was raised Asgardian in a time where the Asgardian's hated and feared Jotuns. The Frost Giant's were their boogie men, the things their children feared, the monsters that killed so many of their husbands and brothers. Loki was raised to hate and fear them just like every other Asgardian child, so when he found out he WAS one? And not just one of them, he was one so small and weak that they left him to die.

That completely broke him. He won't go after the throne of Jotunheim because he HATES Frost Giants. He HAS to prove that he's not some cold brute, some frozen monster, he is LOKI. The Silvertongue, the Trickster.

Could he have done it? Yes. But that would require him acknowledging not only is he a Frost Giant through and through, he's so thoroughly one of them he deserves to lead and guide them. He's an Asgardian at heart, and the only way to prove that is to prove that is to take the Asgardian throne, as would be his birthright as Loki Odinsson.

That blows that Loki was so butthurt about the whole being Jotun thing. Because he really had a good thing going there with that. He really could have overhauled the whole Jotun image and completely set in motion a bunch of new laws and changed education realmwide and set up a completely new system of governance, really brought about a whole renaissance in the cold region. Really...Iceland the place up a bit.

Its just that self loathing...it seems to weak and petty. Why wallow in it? especially when getting over that shit means you can have your cake and eat it too. Its so..unLoki of Loki. He ALWAYS takes the ace in the hole!

It's part of Loki's mainstream appeal, though, finding out he's not only adopted but he was (literally) left out in the cold by his actual parents. As JonSmith said, this leads to his massive insecurity and major hatred of Odin for keeping him as a political pawn (in his eyes). And plus, the Asgardians are pretty much the most powerful race of the Nine Realms with all the cool weapons in their vault (hintINFINITYGAUNTLEThint) so it makes sense for him to want to be king of the highest hill there is.

I think it's an awesome idea! The Jotuns are quite violent so they might even respect that he overthrew Laufey and killed a few of them. Or they could get super- p****ed.

King of the giants in the films or in the comics?

In the comics, the giants have no one king. They are divided in into several kingdoms, villages, or wandering societies. They are either too stupid or chaotic to advance beyond their current state. They also tend to despise Loki for being raised by Asgardians. He is out of place among them thanks to being so short and a son of Odin. Loki also has no real claim to any throne because his biological father's kingdom would have been taken over by another centuries ago.

In the films, Loki would probable suffer similar problems. He would be despised for being a runt, Asgardian, and getting Laufey killed. Jotunheim is also a broken world that is still falling apart from a war that occurred a thousand years ago. Why would Loki want to rule over a dead world when he can rule over one full of life?

In both cases, Loki usually despises giants. They are brutish and crude from a primitive society and weak magics. Loki was raised in the most advanced society of the nine worlds with people he can at least have a semi-intelligent conversation with. He has no real ties to Jotunheim nor any interest to go back to it. For his massive ego it would be an admittance of failure. He thinks he is worthy of the highest throne in the nine worlds. Accepting Jotunheim would be accepting a lesser throne. It would be like if you had a chance to be king of the British Empire at the height of its power, but instead accepted a third-rate primitive society that still lived in mud huts.

Its in his character