Two-Lane Blacktop, one of the best movies ever made (if you ask me).
One of my favorite movies as well, but I would hardly call it slow. It has fantastic pacing and a lot of shocking action.
To the OP, I would say Grave of the Fireflies. I’m not sure how long it was, but the film really took its time and the content was excruciatingly moving.
The Kingdom by Lars von Trier. Although it was originally a miniseries, I saw it in the cinema with all the episodes strung together.
Quite an experience. Recommended.
The Straight Story moved very slowly. Liked it.
Betty Blue (Director’s cut) - has very slow sections, and although there are intermittent fast sections throughout even these tend to be continuous scenes so the pace never really picks up. An amazing emotional rollercoaster of a film with a fairly long, drawn-out and pretty harrowing ending.
I absolutely recommend watching the Director’s cut rather than any other version though - it adds ages to the film but unlike the the edited version which leaves so much out, the ending really makes sense.
That must have been some marathon!
My vote would be Solaris. Nearly three hours long and nothing happens. But it happens beautifully.
Good choices so far – The Staight Story, especially, IMHO.
Ill add Tous les Matins du Monde, and Tokyo Story. And also that German production from last year, about an East German playwright and the secret police guy who is assigned his case.
As I’ve said in another thread recently, I find this movie (and the American remake) intolerably boring. I’ve fallen asleep several times in trying to get through them. Stanislas Lem’s original book (which these both change considerably) isn’t anywhere near as slow and boring.
I thought it was a bit slow, actually. Very good movie, but not fast-paced.
Reds is this exact type of movie.
I adore Gosford Park, which I wouldn’t really call fast-moving. I love all the long, slow tracking camera shots.
I also love the Coen Brothers’ first movie, Blood Simple, which has pretty slow pacing but still mesmerizes me.
I’d like to insert my Jason Boring joke here.
I enjoyed Thin Red Line although it is long and slow for a war movie. Jarhead as well.
Kwaidan. Four Japanese ghost stories, told with great deliberation, in one 183-minute movie.
The Painted Veil with Edward Norton and Naomi Watts was a movie I thoroughly expected to loathe. An upper-class English love story set in a cholera epidemic in China at the turn of the century? Riiiight.
Instead, I found it remarkably well-done, and nicely paced. As it turns out, I DID loathe the movie, but for personal reasons, not due to any failing on the movie’s part. It’s one of those “amazingly well done, but I’ll never watch it again” movies for me.
Gee, hadn’t heard that one before. 
What would people do if Damon hadn’t done the Bourne movies? If people found it “boring” because they expected some jacked-up Jason Bourne thriller spy thingy, it’s their own damn fault. It’s a slow, quiet movie about one man’s slowly losing his moral compass. It’s not a perfect movie (I wouldn’t have minded seeing Jason Bourne pop up just to blow away Wilson’s stupid grown son), but I found it fascinating, and one of the best movies of that year.
Anyway, a lot of the ones I was going to mention have been mentioned, such as 2001 and The Straight Story and The Painted Veil. cymk mentioned The New World, and I’ll go further and say anything by Terrence Malick: Badlands, Days of Heaven, The Thin Red Line (which msmith537 mentioned). Also,
Fitzcarraldo
Dersu Uzala
Wings of Desire
Until the End of the World
Northfork
There Will Be Blood
The Lord of the Rings: The Fellowship of the Ring
The English Patient
The Fountain
Sunshine (until the end, anyway)
Brokeback Mountain
I’m still scratching my head at how City of God is considered either long or slow. It’s longer than I remembered, at 2:10, because I could have sworn it was a 90 or less-minute film. It zipped by so quickly. But also, the memory I have of it is of a constantly moving camera, rotating continuously, and practically non-stop action with lots of gunplay and chase scenes. I need to see it again.
That was the one I was going to mention. I couldn’t stand the movie, but many people think it’s a masterpiece.
I’ll quote one of the rave-reviews, that I found very well written:
Blade Runner.
Go ahead and Pit me if you want, nerds. It’s slow as hell, and took me a few tries over a few years to finally get through. I admit it was good, though. Just slow.
City of God-
Long- yes
Boring- no
Slow moving- no
Actually, I thought I just made it up. 
I didn’t expect a Jason Bourne movie. I just didn’t find it as compelling as I thought I would. It was supposed to be “The Godfather of spy movies” but ended up more like The Godfather III of spy movies.
I’d echo this - I went into it expecting something cerebral but was still bored to tears by it.
As much as I love them pretty much all the LOTR films are a bit too long for their own good. I had a Rings-athon with a friend a couple of years back and it took us two days to watch them whilst not completely tuning out (and she’d not even seen the later two).