romantic vise but mostly immortality wise? I like the fountain of youth plot.. Wich I have never seen in movies but only heard about. I liked that it was about immortality but not a thriller,... it was brain sex as kitty walker would have said.
Titanic (doomed romance, with the message that it's more important how you live than how long you live - other similar messages)
Peter Pan (the heroine has to make a similar choice whether to be young and unchanging forever - with the boy she loves - or live a full life)
Twilight (also deals with a mortal girl getting involved with an immortal family and falling for one of the sons, but unlike Tuck Everlasting it idealizes immortality)
Interview with a Vampire (a particularly brilliant performance by little Kirsten Dunst as Claudia, a vampire trapped for eternity in a little girl's body)
Harry Potter (the theme of immortality isn't stressed quite as much in the movies as in the books, but it's definitely there)
Even though it's a book and you asked for movies, I have to recommend The Declaration by Gemma Malley - along with Tuck Everlasting, it's one of the best and most realistic views of immortality I've encountered.