and the only thing that I remember of it is that someone was wearing a yellow t-shirt. Or they may have been blond. Or both.

the filmmakers you mention all came to prominence during a particularly dull period in American Cinema (late 80's early 90's)when ANYTHING that wasn't Simpson / Bruckheimer et al was praised to the heavens. Directors like Hal Hartley, Todd Haynes, Jarmusch, Atom Egoyan (Yep, I know he's Canadian), Soderbergh have all produced works of ponderous self-importance during this period that have not aged particularly well.
Having said that, I LOVE "TWBB", and do think it's a very "male" film that will stand the test of time and "Broken Flowers" does have its moments, so maybe they're all getting better as they older?

Firstly, I love Dead Man, if nothing else it is one of the most beautiful looking films ever made.

Secondly, I disagree that "there is an increasing trend towards this sort of movie". It's exactly because most Hollywood films are still vacuous dross that anything a little more awkward gets so much attention.

There Will Be Blood is a very familiar single character's rise and fall story which although told with a modern sensibility is hardly a similar movie to ones which reject familiar narrative structures.

Paul Thomas Anderson who directed it has directed a series of interesting movies some which have been within familiar narrative structures and some that have been outside them. In my opinion he is a wonderful director. There Will Be Blood, Magnolia and Punch Drunk Love are all amazing films, with quality writing and quality performances, and Boogie Nights has many good things about it. There Will Be Blood and Boogie Nights out of all of PTA's films are his most conventional.

If you were going to address the strange plotlessness of films then Magnolia or Punch Drunk Love would have been more logical choices, although I would have disagreed I would have understood why you'd reached that conclusion.

As for the central question: What is it with the "awkward" American films that fascinates people so much?

I would argue that these films are one strand of film, you could call it art house or experimental or whatever, one that has been around for years and has produced some amazing films such as those of PTA and a couple of Jim Jarmusch films (e.g. Ghost Dog, Down By Law) and some awful films (Anything by Gus Van Saint, some Jim Jarmusch films, etc...).

This strand of films can no more be dismissed than Action Films, Police Procedurals or whatever... for each genre will produce great work and poor work.

This strand is nothing new and it is definitely not very dominant. You mention Coppola's Rumblefish for example, hardly a modern director. Within this strand of film you have sub-strands, so you have arthouse comedy such as Wes Anderson, and nowadays you have mainstream arthouse such as Juno or Little Miss Sunshine, or indeed There Will Be Blood.

And it isn't just am American phenomenon, the French do it too (See Jean Jeunet's Delicatessen or Amelie) for example, as I'm pretty sure do most western countries. In fact considering the history of film you could argue that this sort of film is very European in it's sensibility.

The current success of some of these films is really only due to the style having become completely absorbed into the cultural palette, people enjoy the style now, it is familiar to them, and so now the limits of the genre can be explored within mainstream pop culture. Whereas before it was more a niche sport.

People like to feel awkward. It's something that is universal and when done right it hits peoples nerves and provokes a reaction. But not everything is for all people. Gus Van Saint for example is not for me, he makes awful and boring, and yes pompous and pretentious works of twaddle.

But There Will Be Blood has more in common with Citizen Kane, The Godfather or Goodfellas than it does with Elephant, and it is much better for it. In fact the reason I prefer it to Kane and The Godfather is precisely because the epicness is filtered through the aesthetics of "awkward" cinema. It speaks much more to me because of that.

I haven't seen Dead Man. I don't really want to as Jim Jarmusch has become a bit of a parody of himself in some ways, and his refusal to have a plot does really grate on me sometimes. But his best work is good and so I'm happy he keeps on trying. Just as Terry Gilliam at his best is so fantastic that you can forgive him the Imaginarium Of Doctor Parnassus and Brothers Grim.

Basically what I am saying is:

This kind of cinema is not new. It is not dominant. It is not particularly American. And it is important that it gets made because it is one of the ways of mining the human condition. I'd rather people made mistakes than didn't make anything at all. That said these sorts of films can be as formulaic as a brainless action movie, with none of the fun chase scenes. So it is, as always, a fine line.

Well, I thought both Dead Man and There Will Be Blood were great films. I also know several people who thought they were rubbish. Largely because, and I quote, "nothing happened" in them.

Whilst I would disagree with that suggestion, I can understand where they're coming from in the sense that they're not your traditional ABC Hollywood narrative. However, I was gripped from start to finish.

Both films just seemed to have a certain atmosphere that kept me transfixed, and that was due to a number of things - performances, cinematography and, by no means the least important factor, one hell of a soundtrack. A straight forward narrative is not the most important factor.

It's possibly worth noting that I saw both in a decent independent cinema. That still counts for something when watching non-blockbuster fare.

...he is completely wrong on Jim Jarmusch who is quite clearly a genius. If you seriously think that "nothing happens" in a Jarmusch film, you're not watching properly.