Nikon D610 has a Nikon F lens mount and currently there are 274 native lenses available for this mount.
Nikon D610 doesn't have a sensor based image stabilization system but 53 of these lenses already comes with optical image stabilization.
Since Nikon D610 has a Full frame sensor, it has a focal length multiplier of 1× so lenses will provide their original focal length on D610.
You may also also be interested in these:
Nikon D610 Lenses with Image Stabilization
Nikon D610 Lenses with Weather Sealings