[Boromir88]

I'll get to all the lovely speculation in a bit. But, I think at first I'm going to have to use a few quotes here... I'd first like to note that there certainly does seem to be 'capital punishment' or a 'laws' within both Gondor and Rohan.

People tend to see treason as a very serious offense that back in the days (I don't know much about it's punishment today) but that certainly sent you to death row. Treason was a big no-no, and I think it was a big no-no in Middle-earth as well. In the instance with Beregond, Aragorn had every right 'by law' to take Beregond's life for betraying his service to his Lord Denethor (as well as actually killing people):

And the King said to Beregond: 'Beregond, by your sword blood was spilled in the Hallows, where that is forbidden. Also you left your post without leave of Lord or of Captain. For these things, of old, death was the penalty. Now therefor I must prounounce your doom.
'All penalty is remitted for your valour in battle, and still more because all you did was for the love of the Lord Faramir. Nontheless you must leave the Guard of the Citadel, and yo much go forth from the City of Minas Tirith.'~The Steward and the King

So it certainly seems Beregond's treason against Denethor and 'spilling blood in the hallows' would get you capital punishment. However, Aragorn decided to expel Beregond from the Tower Guard and from Minas Tirith (though gave him comfort in making him a Guard of Faramir. Which I would also guess that if not executing a criminal for a serious offense the next serious punishment would be to expel them from society...where it just so happens to Smeagol:

'No one ever found out what had become of Deagol; he was murdered far from home, and his body was cunningly hidden. But Smeagol returned alone; and he found that none of his family could see him, when he was wearing the ring. He was very pleased with his discovery and he concealed it; and he used it to find secrets, and he put his knowledge to crooked and malicious uses. He became sharp-eyed and keen-eared for all that was hurtful. The ring had given him power according to his stature. It is not to be wondered at that he became very unpopular and was shunned (when visible) by all his relations. They kicked him, and he bit their feet. He took to thieving, and going about muttering to himself, and gurgling in his throat. So they called him Gollum, and cursed him, and told him to go far away; and his grandmother, desiring peace, expelled him from the family and turned him out of her hole.'~Shadow in the Past

Eventhough Smeagol was not a Hobbit, he was very similar and related to them, so I would guess that their laws and punishments would also be rather similar. If there was a really bad trouble-maker that did some serious crimes, expelling them from society would seem to be the worst punishment one could get (as happens what happens to Smeagol). As I agree I simply can't imagine Hobbits having capital punishment.

Also, in Rohan remember Eomer had been jailed for treason and my guess was his punishment was still waiting to be decided:

'It is true,' said Theoden. He had rebelled against my commands, and threatened death to Grima in my hall.'
'A man may love you and yet not love Wormtongue or his counselsm,' said Gandalf.
'That may be. I will do as you ask. Call Hama to me. Since he proved untrusty as a doorward, let him become an errand-runner. The guilty shall bring the guilty to judgement.'~The King of the Golden Hall

Definitely in Gondor and Rohan crimes such as treason and murder would most likely send you straight to capital punishment.

Treason was a very serious offense way back into our early history to the last time I remember all during the Cold War. I wouldn't doubt it if it's still seen as a serious offense today that warrants death. The idea of 'betraying one's country' isn't taken to lightly, especially in war time.