No, not for romantic relationships, although I have felt affection for NPCs who have a strong bond via friendship, brotherhood or non-immediate family.
I'm only thinking of GTA IV here, but that game and it's expansions I have developed affection for the NPCs that are important to the protagonist you play, e.g Roman, Brucie, Little Jacob, Packie, and Dwayne from GTA IV, Clay, Terry and Jim from The Lost and Damned and Gay Tony, Armando, Henrique and Yusuf Amir from The Ballard or Gay Tony.
I don't quite know what it is about Rockstar games and these characters, but I found it easy to emphasise with the friendships and affection the protagonist feels towards these characters that elevates them above mere NPCs and quest givers.
Maybe it's the lack of strong characterisation and good writing, but I've never played a game in which I've felt as affectionate towards a romantic relationship as I have towards the strong friendships, not even in Red Dead Redemption in which, although I could emphasise with John's motivations and recognise the importance of his family as a concept, when I finally got around to meeting Abigail and Jack, I didn't feel much affection towards them beyond recognising John's own feelings.
Thinking about it, it's probably humour that makes me feel affectionate towards an NPC, because in Fable III I felt more affectionate towards the funny NPCs than I did my own family that I created and had ownership of.
Indeed I actually spent more time interacting and taking ownership of the more amusing NPCs, who you could lead by the hand and who would wait wherever you left them, so I transplanted a lot of the more amusing, more outrageous NPCs by leaving them in the various pubs around Albion, in which they would stay forever and constantly get hilariously drunk.
There's one particular Mercenary voice/personality type who's an absolute riot when they gets drunk, so I made sure each town and bar had one of him in it (and I had a few at the palace to keep the nobles in line).
Also, there's one type of male Auroran NPC who has an amusing one-liner Easter Egg if you go to the effort of taking him from the alcohol free Aurora and leaving him in a pub in Albion, then waiting around to observe his default NPC pub behaviour. He'll go up to the barman and say "A Crocodile Cocktail... and make it snappy!".