I have just taken a set of Goodyear Assym2 tyres off my MFL 2.0 Estate with 225/55R16 size.
They had around 4mm of tread left and up until about 4.5mm they were fine. If provoked, the front would let go on a corner and then it simply slid until it could find traction. Less than 4.5mm I found that the back end would light up if moving off smartly from a side road and would get skittish in the wet a little earlier than before.
I have just fitted a set of Bridgestone RE0002 Adrenalin tyres and they really work well. I have them on 2 of my other cars and they just grip in the wet.
I also had previously a set of Dunlop SP Sport 01 and they were nice, but wore the edges (even though tracked up from WIM) and were also lousy in the cold (near freezing) weather and a set of Goodyear EfficentGrips which I had no issues with.