Canon 60D has a Canon EF/EF-S lens mount and currently there are 290 native lenses available for this mount.
Canon 60D doesn't have a sensor based image stabilization system but 91 of these lenses already comes with optical image stabilization.
Since Canon 60D has a APS-C sensor, it has a focal length multiplier of 1.6× so you have to multiply lenses original focal length with this multiplier to find the Full Frame equivalent focal length of the lens when mounted on 60D.
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Canon 60D Lenses with Image Stabilization
Canon 60D Lenses with Weather Sealings