Begotten definitely. Confusing and simply hard to stomach. Although an easy-to-follow allegory to Jesus Christ and the violence of mankind, the confusion mostly stems from the interpretation of that story and how it is presented.
Eraserhead is up there too. I'm not quite sure why people think of it as bullshit- it was quite impressively directed considering the budget and limitations.
The Room is confusing in an absolutely hilarious "wtf, this movie is so awesomely bad" kind of way.
I'm personally intrigued by how much Christopher Nolan's Memento and Inception have been mentioned in these kind of discussions. I love both movies (they easily make my top 50 list) but I'm not sure why they are seen as confusing, personally. I think there is a difference between genuinely confusing and just intricately plotted and layered. Memento's narrative is unusual, certainly, but it's overall plot is easy to follow and after seeing the end it's very easy to understand the character motivations and any other previously confusing aspect. Inception I'm more confused about people's confusion (and I can't express this without sounding like a pompous asshat, but oh well, hooray for first posts establishing pretension).
With Inception (oh, and potential SPOILERS!!!!!!!!) it clearly defines the properties of the dream world when Ariadne (Ellen Page) first enters it. Sure, the plot at the end is quite literally layered but all of it at that point is essentially 3 action sequences stacked on each other. Sure, the deepest layer is somewhat confusing in terms of understanding the mechanics of the ending, but as soon as you realize that at that point the plot relies on understanding of the characters (who are quite well-defined) it isn't that difficult.
2001 is up there for me. Well, just the last 20 or so minutes of it I suppose.
Primer was simply amazing for such a small budget and as a directorial debut. Definitely one of the most genuinely confusing experiences without falling into that "attempting to be confusing out of gratuity" issue that i feel is present in a lot of the movies previously mentioned.
The Cabinet of Dr. Caligari, I suppose.
I was confused as to why Casablanca is loved as dearly as it is. And confused as to why there are so many Saw movies (I understand its for the money, I guess I'm just confused as to why people give it so much money).