Many steel coasters have upside-down elements, but as of 2012, there aren't any wooden coasters that include inversions. That's going to change in a big way next year, however, as there will be three (count 'em three) woodies that will send passengers head over heels. Technically, two of them, Iron Rattler at Six Flags Fiesta Texas and Outlaw Run at Silver Dollar City, will be wood-steel hybrids and will incorporate steel into their tracks.
The third, Hades 360 at Mt. Olympus Theme Park, will maintain its traditional wooden coaster track but will swap out its trains for new Timberliners. The unique trains hug the tracks in a different way and, apparently (hopefully?), make inversions possible. You can read about the (wonderful) Timberliner trains in my review of the (non-inverting) Wooden Warrior coaster at Quassy Amusement Park.
You can also read about the newfangled woodies and other new rides coming next year in my Roller Coaster Ride Guide 2013.
Photo: Mt. Olympus Theme Park.