In the band I used to be in we did have some country tunes, but they were all modern country. Most of the time we'd start off a show with Here for the Party by Gretchen Wilson. That was a fun song to play. The main riff requires the guitar to be in drop D. I created my own solo for that song, but the solo had more of a rock feel than a country feel.
Another one of the modern country songs we did was Before He Cheats by Carrie Underwood. That is what I call, "A Pissed-Off Girlfriend Song." The ladies used to jump to their feet (if they weren't already on their feet!) and sing along quite enthusiastically to that one!
We had quite a varied set list. We'd do modern country, Motown, R&B, funk, classic rock, modern pop, and a hair metal song or two. We even did some go-go.
I suppose the most "classic" style country song we did was Five O'Clock Somewhere.