I've given villagers golden beetles when they ask, but I don't think I've ever given away unorderables. I generally don't care what my villagers houses look like except for Sly who I like to keep with a general jungle/rugged theme and lolly who I like to keep with a kitchen/library theme. I don't have much of a reason to give expensive stuff, the cheap crap keeps them just as happy.
I gave Nibbles sketchbook without knowing is unorderable and now it is missing!! LOLL and I also gave some real rare thing to my other villagers whom I gonna keep permanently~
I shook a gorgeous item out of a tree once and gave it to Merry when she asked.
One day Marcel was asking for a 1x2 item to replace his [item of similar size] and I could not find a spare 1x2 anywhere either in the shops or the trees or in my storage, so I went to the island and they had a mermaid couch - I gave him the mermaid couch. He gave me his pic in return so that was cool.
Those are the only rare ones, I think. Usually when they ask they just get whatever equivalently sized crap's in the shop that day.
I also gave Wii Balance Board to some villagers but I'm not even sure it's expensive because last time I bought it back for 500 bells from Jacques(more of rare I guess).
I gave some gracie furnature a few times and some reorderable dlc but nothing more expensive then that. Usually I just give them crap but now I'm starting to hate how crappy their houses look so I've started to buy furnature sets for every character and give them items from those sets so it's less of an eye sore.
Last night, Pompom told me her house looked sad (and it really did, she has totally decimated it) and she needed a really big piece of furniture. I went and got my gorgeous bed out of my house for her. Today, I was surprised by her birthday, and I had a royal crown on me, so I wrapped it and gave it to her.
Winnie was partying with her, so I guess my being worried that Pompom wouldn't want a second peppy in town was for naught.
I gave Truffles my only lovely phone ... and she didn't keep it, that's why I kicked her out after (jk, I just wanted a new peppy villager). Also gave some Gorgeous furnitures to Lionel and Muffy because they have expensive tastes