0.5 points I've noticed that pro games with differences of more than 3-5 points are rare--that is because pros will resign when they know they can't catch up, and they're good at counting (although there are occasions of miscalculation--there is a thread about Lee Changho--arguably the greatest player of the past 15 years or so--resigning while ahead).

The question really isn't answerable, but I'll give you my subjective, un-scientific thoughts: It depends on who is playing--both the general level of the palyers and the difference in strength. If I play a pro in an even game and lose by 50 points, I would call that a well-fought game for me. If I'm playing someone around my strength or with proper handicap, I'd say around standard komi (6.5 ish) is a fairly close game (at pro level, that is a "wipeout"). For DDKs, 15-20 points in an evenly-match game is still not a complete blowout. (This is all based on 19x19 games, by the way.)

But these are just generalities--I depends on a lot of factors, I think, including how the game goes.

For me, anything less than a 4 or 5 point margin is pretty close.

Ay 5k, 10 points might be close.

less than 15k, 20 points might be close.

At any level you might have a game in which you lose by a liberty-- this typically results in a double digit point loss, but I think you can still consider the game as having been close.

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Somewhere around 5-8 points, I could consider close. I don't count enough..

It is not uncommon to have a very close, well fought game that is actually not close in points, or where one player resigns. There may be a very complicated fight where two large opposing groups are fighting for life. That fight could be very close, but because one large group dies and the other lives, the point spread in the game could be really big (the player on the losing side of that fight would typically resign.)

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That's correct, and conversely, it is also common to have a game with a seemingly close score, like 3 points,
but where one side was leading and controlling the game from the very beginning and the other side never had a chance.

In other words, point spread and Level spread are not always correlated.

The games I feel are the most amazing are the ones where my opponent (or the two opponents, whoever they are) have a gigantic battle all over the board, with massive exchanges happening and dead groups on both sides... but rather than resignation, when the dust settles the score is within 5 points.

Doesn't happen *too* often in my games, but man, it's a great adrenaline rush on top of the one I just had from the fight to count just at late endgame and realize that after a huge furikawari, it still comes down to a half-point and I have to maintain sente for the next 15 moves to be certain of winning.

I don't think you can define it in terms of point difference. As Fwiffo said above there could be a huge, exciting battle between opposing groups with the inevitable result that one of them dies, resulting in resignation. I think quality of play figures into "well fought", too. If one side makes a blunder and the other side returns the favor later on, evening the score, I wouldn't call that well fought. And the "fight" might just be delicate and subtle maneuvering with no invasions or captured groups, something some people might not call fighting at all. Then, too, what about a game where one player suffers a big loss and bravely persists, gaining slowly but not quite catching up at the end? A great game to study is Dosaku (W) vs. Yasui Shunchi (2 Stones) played 19 Nov. 1683. Dosaku ended up losing the game by one point. The game is considered Dosaku's lifetime masterpiece and it is also Shunchi's lifetime masterpiece. That is a well-fought game!