Best to exclude integrated gfx from this thread, and only systems that are used multiple times a week, otherwise there will be some shockers.
I'm still using AMD HD5470M in an old laptop used for watching Youtube in the kitchen. It's that old that it's the previous Radeon 5000 series, not the new one
Probably slower than that Quadro. The laptop is kind of knackered though, broken keyboard so have to use external keyboard, HDD runs at 100% utilisation nearly all the time so it is ultra slow. When I get round to it, I plan to replace this system with a desktop running a 8800GTS 320MB.
edit: In terms of worst GPU used regularly for gaming (as might be more interesting), my son is using a Radeon HD7950 I bought in 2012 before he was born.