I don't listen to too much modern country, aside from the occasional twanging it sounds too much like generic pop for me.
That said...
Patsy Cline has one of the most beautiful voices I've ever heard and her singing "Walking After Midnight" is one of my absolute favorites.
On the other side of that coin, I like Don Williams voice as well. It's just so smooth and relaxed. I know that sounds stupid, but that's what I came up with.
Willie Nelson is also a favorite of mine, but his impromptu picking has a tendency to get annoying. Not that I don't appreciate fine improvisation, but sometimes it throws the song off.
If you want real deep from the hills country music, I like Ralph Stanley and to lesser extent Dan Tyminski, you might have heard his stuff in O' Brother Where Art Thou? soundtrack.
There's a bit more, but I'll end with this.
This is kind of embarassing, but from the modern stuff, I kind of like Diamond Rio. The songs aren't that great and have a tendency to sound like the 'generic pop' I mentioned, but they can sing although they get a bit carried away a bit.