1,955 hours across six years and 74 of my 237 owned games. 1300+ in TF2 alone, although 4-500 of those were back in the days of idling/farming. Second place is the original Binding of Isaac with 120 hours, and the remake will retake it inside the next day or two with 119.
Things inflating the count: TF2/card idling
Things not counted: Games I played before I owned them on Steam (largely, the older GTA games, Oblivion, and Lord of the Rings Online), games from Humble Bundles, etc. that were played on Linux before the official Steam for Linux, or that didn't have Steam for Linux versions (probably another 50 hours on Binding of Isaac, at least a few on Dungeons of Dredmor and Beat Hazard Ultra), gameplay in offline mode, time spent playing Steam versions of the Genesis/Mega Drive classics (it seems to only count time in the launcher)