Skyrim should have a Thunderdome.

Bingo.

Beat me, but I would prefer a more co-op variety of multiplayer, perhaps you could still fight your pal in the arena. Would make some good RP.

Anyway.
I like Shadow28's idea, perhaps grunts on grunts for each side to entertain the populace and to get warring done.

I think the Arena's concept is good but it can be improved for sure. Actually the feel I got from the "arena" in The Pitt in FO3 was already better than OBs so I think Skyrim's (if there is one) will be even better.

Personally, I think that is how war should be handled. The people who want war go to an arena or a boxing ring, whatever, and fight to the death. The one left alive is the victor. But that'd never happen, people aren't that smart.

I think level scaling ruined the arena experience in oblivion. You shouldn't be able to become champ until you are a high-leveled character!
And if there is an arena in skyrim it personally think it should be related more to rivalries between different houses/factions like in DA:O but also with elements of entertaining the general population.
That being said pub brawls would be a lot more fun and/or "western" like challenges in various locations (no interference from guards)!

Maybe a decent-sized one in one of the cities, but more small barfight-ish fight clubs.

I want to see arena without the ranking system. Oblivion made it a faction quest, but I think that's unnecessary; all these talks and wasting time listening to "Good people of IC..derp derp".
When you just want to whack some people, you'd visit a local arena for a fight. You just get in there, and the door shuts behind you. You get random opponents scaled for your level, and you can loot...if you win. Depends on places, you might even get multiple opponents coming at you at once or taking turns.
There would be a big colosseum with thousands of people watching, and also many smaller arenas across the land. Some of your local taverns have small places where people can have a fight for money. Sometimes you can even participate in a street fight with a random NPC.
Bigger arenas have tougher opponents, so unless you're confident with fights, you'd stay away from them.

First of all, I will go ahead and say it: I play D&D. All I can say is don't knock it till you try it, it is extremely fun. (But don't play with the grid, it is stupid)

When my group goes into large cities, we usually find some form of an arena, but guess what, it is not just single fights one after another with payment in between. We go through long arduous tournaments.

Example: 7 round arena we recently did for dwarven made adamantine weapons (does not get much better) and 5000 gold each (a moderate sum of money). First round, six orcs come running at us, and swiftly get owned. Second Round, three Bullets (sand burrowing, spiky creatures) attack from under the arena. Third round, 2 rust monsters attack from a cage (monsters that eat metal weapons and armor). Forth round, 35 kobolds (2 ft. tall lizards with 3 ft. tall spears that are some of the weakest enemies in the game) attacked and our group tank killed them all with a move called greater cleave and throwing them to the spiked cage ceiling. Fifth round, invisible stalkers (invisible monsters that try to murder you) attack. Sixth round, A hydra attacks from a cage, our tank proceeded to through a halfling (4 ft. tall half demon creature) into its mouth where he used his swords to rip down its neck, and upon reaching the stomach, cut its way out killing the hydra by releasing its own stomach acid on it. Seventh round, the grand champion attacks.
The grand champion is a 4'3" dwarf with two jewel encrusted giant battleaxes of adamantine metal. he immediately runs out, rolls out of the way of two kobolds that fall from the ceiling, and keeps running. The group mage casts a lightning bolt at him, and he casts the same spell back, counteracting it. The tank tries to duck down to cut at his legs, so the dwarf uses his axe to hook the tanks head and pull him to the ground, and proceeding to jump off of his shoulder. He then runs past another mage who uses his magic to raise the rust monsters as allies, going straight for the one who cast lightning. Me, the group archer, proceeds to shoot 18 arrows at him from atop my pet dire lion (lion the size of a small house), and one of our fighters tries to attack him, but he knocks both of his weapons out of his hands, and keeps running for the mage. The Rust monsters reach the dwarf and eat his weapons and the studs on his studded leather armor. Uneefected, he continues to the mage whom he releases a huge punch at which sends the mage flying backward. He continues to run, but is stopped by the tank who has stabbed him in the spine from behind.

I want fights as epic as that.

Specifically, I want multitudes of small dirt rings where you do fist fighting. Then there should also be minor arenas here and there, and the capitol should have a huge arena where you can compete in multiple tournaments like described above.