My vote goes to Lonesome Dove. I bet I have watched the entire thing about a dozen times or more. I've seen ALL the various other "chapters"... Return to Lonesome Dove... Dead Man's Walk... Comanche Moon... Streets of Laredo... all are good but the original is a masterpiece for the ages. By far, my favorite role of Tommy Lee Jones AND Robert Duvall.
It was good, that is for sure, but I think Shogun is the best for regular TV. Now it is by far Game of Thrones.
GoT is a series, I don't think it qualifies as a mini-series.
A series is or was 27 episodes. And, they are open ended. They have no set end date. GoT has a set number of episodes based on the books and once they diverged from them they set a hard and fast end sequence.
A series does not have a set number of episodes. I admit the definitions are often vague, but the simplest one I've seen for mini-series is a show with a set, pre-determined number of episodes. GoT did not have a pre-determined number of episodes when it began; I don't think the number of seasons was determined until the show was done with multiple seasons.
I've seen mini-series defined as only having 4-6 episodes, or of having at least 2 but fewer than 13 episodes. On the other hand, I've also seen mini-series defined as just not being open-ended.
Based on my own experience, GoT is a series, not a mini-series. It's certainly one of, if not the best shows currently on, I just wouldn't call an 8 season, 73 episode show "mini."