When wife and I had our 'new' home built 20 years ago, we opted to have hardwood floors on the ground floor, so we have been battling this issue ever since. Sadly, we haven't found a good solution.
The stick-on felt pads work fine, but over time they slip off the foot of the chair. I think the issue is that the force on the pads is not straight down through the chair legs, as you might expect, but rather includes a component that wants to shear across the face of the pad, and over time, this causes the pad to slip. Always toward the back of the chair which suggests that shear force arises because the weight of a person sitting on the chair isn't applied equally to the front and back legs. Anyway, the result is that the pad eventually comes off, and then resticks itself to the floor. Mineral spirits will remove the adhesive from hardwood floors - DAMHIKT.
Mattias Wandel says that the permanent solution to that problem is to use felt pads without pressure-sensitive adhesive, sticking them to the chair using hot-melt glue. Rather than using a glue gun, he suggests heating both the chair foot and the pad with a heat gun and then smearing a glue stick onto the foot. Haven't tried that.
We've also used rubber feet that have a recessed hole for a wood screw that attaches into a hole in the chair leg. They work OK, but over time the rubber wears down to the point where eventually the head of the attachment screw becomes exposed and scratches the floor.
