The capital of China is 北京, which in Mandarin Chinese is pronounced [bejʤiŋ] (using the voiced symbols for what are, strictly speaking, voiceless unaspirated consonants). bayjing would be a pretty good English folk spelling. For mysterious reasons, this word is routinely mispronounced by newscasters and other people who are supposed to know better.
I just heard yet again on TV the pronounciation [bejʒɪŋ], where the sound at the beginning of the second syllable is the one we might write as zh in folk spelling, that is, the sound of the s in words like measure and pleasure. Ever since newscasters and the like switched from Peking to Beijing I've been hearing this mispronounciation, and it drives me crazy. I'd understand if they were just adapting the Chinese word to the sound system of English - I don't expect them to learn Mandarin - but that's not what is going on. English speakers are perfectly capable of pronouncing [bejʤɪŋ]. [ʤ] is a common sound in English. It's the j of jaw and the dg of nudge. If you can say budging you can say [bejʤɪŋ].
So, why is it that we so often hear [bejʒɪŋ]? The only hypothesis I've come up with is that it is because the sound [ʒ] is somewhat exotic in English. It isn't very common, and as far as I know, all of the words that contain it are loans from French. So perhaps people think that [bejʒɪŋ] sounds more exotic than [bejʤɪŋ] and therefore that it is more accurate. If anybody has a better idea, I'd like to hear it. And if any newscasters are reading this, stop saying [bejʒɪŋ]!
[Update: Lameen Souag has pointed out a parallel example: Azerbaijian, in which the j represents a [ʤ] that should pose no problems for English speakers, is sometimes pronounced with a [ʒ].]