Thanks for all of the answers so far.
My own first thought had been Casablanca, but it occurred to me that the story there turned into some kind of “love of the cause” and “love of country” thing, more than the simpler (and less political) love between a man and a woman. So I decided against that.
I recall really liking Shakespeare in Love in this genre, but I can’t for the life of me recall any of the plot now. So it’s hard to point to that and say, “Definitely that!” I enjoyed Love, Actually, but once again I can’t recall much about it. It also seemed kind of lightweight.
I had thought of Love Story (for the obvious reason, obviously) but discounted it, I guess, for obviousness. (In any case, I liked An Officer and a Gentleman better, anyway.)
Out of Africa was good (maybe The English Patient, too, but it’s been a long time since I saw that one – memory, again). I only saw OOA recently, so that would be high on my list. I liked the way the love story in that developed slowly and persisted over so many years and changes. That I liked a lot.
But I also liked Moonstruck, which no one mentioned, and Moonlight Mile (maybe I’m a lunatic, after all). I’ll have to catch Moonrise Kingdom and complete the trifecta now.
But thinking of New England… I also liked Cider House Rules for the love that ran all the way through it.
Guess I’ll have some movies to watch – alone – this winter. Thanks again for the responses!