Garden State
 
This is an instance where I wasn't terribly interested in seeing the film, but I walked in from another movie just to watch a few minutes out of curiosity.  Within 5 minutes or so, I was totally digging it enough and thought I ought to leave immediately and see it from the beginning another time; but it just kept pulling me in and I couldn't leave. 

As of this posting, I still haven't seen the first half hour, and must acknowledge the possibility that the considerable chunk I missed could have been awful, and maybe it only got good from the moment I walked in.  Nonetheless, what I saw I liked enough include as one of my favorite films of the year 2004.