I'm not sure I can sit through any Star Trek films any more ... and I own a few of them, still (Wrath being one). That being said, I saw the original episode with Ricardo Montalban the other week (they are re-running all the original episodes on BBC2), and it was surprisingly good. (When the original episodes are good they are okay ... when they are bad they're even better. If you're in the mood.)
Apocalypse Now, I'd watch the Redux version (although I haven't seen it, only the original). Brando was so self-conscious about his weight he wouldn't permit any proper shots of him, just silhouettes and close-ups of his face. Also the Redux version has a lot more stuff added, including a risque scene with the Playboy models and the price they have to pay to escape the riot ...
La Dolce Vita you'll love this, it's right up your arty-alley. Not that Fellini isn't excellent, just that you'll get more excited than perhaps you should.
Fahrenheit 9/11 (Parts of it.) I can't recall if I've seen all of this; regardless, only see it when you need some dark humour about the standards of US critical thinking.
Secrets & Lies absolutely fantastic (if very bleak) film; you won't want any popcorn, but you'll certainly know you've experienced a little bit more of life when it's finished. Mike Leigh is fantastic.
The Wind That Shakes the Barley is a(nother) sensational film; I tried watching it on the plane last year and gave up (no noise-cancelling earphones and a dialogue-intensive film don't mix); I've seen a piece with Ken Loach where the interviewer (either deliberately or not) challenged the brutality of the British soldiers depicted in the film; he responded with chapter and verse from the military advisors he had to remove all doubt about the accuracy of the appalling tactics that were (and in some instances still are) used.