This happens to me fairly often, but for varying reasons. One of the most common for me is because I end up associating a memory in my life with the song, usually either a really sad or really happy one. I’m not really sure if that fits with the idea of the thread though since it’s probably at least as much to do with the memory as with the song.
There are some songs that, in their own right, invoke such a powerful emotional image that they can bring on that intense emotion in their own right. A recent example of this for me would be Everything by Anthema, painting a picture of teetering on the edge of falling into despair, but instead choosing to live and to love. Hell, a lot of their songs do it, but that’s off their newest album.
There are others that are just so purely beautiful that they simply bring forth the tears in awe of that. Though these are rather rare since so many songs these days have lyrics, and the lyrics either add to and invoke that emotion, or they aren’t up to par and detract from it. The only real example I can think of like this would be some of Tarja Turunen’s work (either with Nightwish or on her current solo career) as she has an amazing voice and can bring a lot of emotion to it, but is also able at times to be purely, musically beautiful at other times.
And, of course, there are those that have both. A recent example of this would be What Could Have Been by Novembers Doom. It is a relatively simply acoustic piece with a duet between Paul Kuhr and Anneke Van Giersbergen, and if you don’t know who she is, well, she quite possibly has the best voice of any woman alive, seriously. But on top of that, it powerfully calls upon imagery that they’ve built up over their career, the love he has for his wife and his daugter, that saved him from his own death a few years back, and yet in this song, he explores a father and mother grieving the death of their child. I can’t imagine how anyone could listen to it and not be moved to tears.
As for the prefered sex’s voice, I can certainly say that almost all of the voices I would describe as beautiful are women’s voices and so they’re more likely to bring that raw beauty to the song. OTOH, I often find I can relate a lot better to a male voice, particularly one that is in my range (being a baritone, it’s less common, so it stands out). In some cases, I can even imagine a woman and a man singing exactly the same lyrics but affecting me differently. In fact, I have heard a few cases where a love song, for instance, was covered by the opposite sex, sometimes with a couple appropriate words changed (ie, he to she, etc.) and it has a very different feel to me.
That said, if it’s going to be vaccuous, and likely bad anyway, like a lot of pop music, then yeah… I’d prefer to hear a woman sing over a man.