Not sure that I have a favorite, but I have (or have had in the past) least favorites.
The leader of the least favorites used to be KY 30 coming off I-75 at London, used for returning from trips to the south or southwest. The road was narrow, hilly, and curvy, and riding in the back seat of the family car as a kid was a nauseating experience (literally).
Over the last 20 years, the old 40-mile stretch has been relocated onto a new, modern, shorter alignment. The last section opened in February. I have yet to take a trip that utilizes the entirety of the new route (I drove the newly-opened stretch between KY 847 and US 421 back in February shortly after it opened) but it will certainly make me dread that last part of the drive a lot less.
Increasingly, I have come to dislike the route home from the southeast -- specifically, the part that involves KY 15 between Whitesburg and Jackson. It's a reasonably scenic road, and pavement projects have made it a lot smoother in recent years, but it just seems like a very long 60-mile segment. I drove it so often there for awhile that what was once a treat has become a chore. And then when you add on the fact that the portion from Jackson on home is the route i drive to and from work, there's nothing thrilling about it.
I'm also coming to tire of the two routes that I use that lead from I-64 to my home area, US 23/US 460/Mountain Parkway, and KY 7/US 460/KY 205/Mountain Parkway. All of the former is a modern route, and most of the latter has been rebuilt in recent years, but they've still lost some of their charm.
The only other real candidate is the US 25E/KY 11 corridor. If there's lots of traffic in Middlesboro, 25E is a PITA with all the signals. Cops like to patrol between Pineville and Barbourville, so watch your speed. And KY 11 between US 421 and KY 66 at Oneida is in terrible shape.
The routes from the west are ones I use for most of my non-leisure travel so I'm not sure how to count them.
Part of the drudge of travel is that you start running out of new ways to get to new places. As beautiful of a drive as it is, I've gotten tired of I-68 simply because I've been on it so often. Ditto Alternate US 58 between Norton and Abingdon, Va.