disregarding the fact that they may also watch motion pictures, and TV dramas as well from different regions. .
I place live action stuff in a different area. for me there's a real disconnect between seeing a Japanese/Chinese/Russian/Whatever onscreen speaking English that doesn't match their lips.
If I go to see an American film here and it's dubbed in Japanese, I'm incapable of enjoying the experience because I know that Tom Cruise or whoever is supposed to be speaking English. They're a real person and with that they bring real expectations.
Animation and games not so much, but like I said, location and setting are important too. If I'm watching an anime that takes place in America starring a bunch of Americans, it throws me off watching it in Japanese, so in that case I'd prefer the dub provided it was good. If I was playing Yakuza, I'd prefer to play it in Japanese because it's easier to be engrossed in the setting.
Though I suppose I'm in that weird zone of knowing both languages.
As for examples, I try to make it a point not to play stuff that makes my ears hurt, but recent Level 5 games are a great example. Professor Layton vs Ace Attorney was absolutely terrible in this respect. Phoenix and Maya were played by "real" Japanese actors and the voice work was dreadful. Nearly ruined an otherwise great experience.
Likewise, Ni no Kuni in Japanese is complete shit, again for similar reasons. Those are the most recent ones off the top of my head though.
That being said, I can totally understand switching to Japanese because an English dub is so bad it distracts. Even if the JP voices aren't that hot, it's not a problem if you don't notice it.