Canon 6D has a Canon EF lens mount and currently there are 268 native lenses available for this mount.
Canon 6D doesn't have a sensor based image stabilization system but 59 of these lenses already comes with optical image stabilization.
Since Canon 6D has a Full frame sensor, it has a focal length multiplier of 1x so lenses will provide their original focal length on 6D.
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Canon 6D Lenses with Image Stabilization
Canon 6D Lenses with Weather Sealings