If you want visible abs you gotta burn calories. A combination of weight training and cardio will do the trick for that. You also must eat well, and clean.

Core muscles are engaged in mostly all exercises, so it's a good idea to do your workout for the day and THEN add on some core work to further challenge your core muscles.

Depending on your body, some core exercises can be more risky for injury, usually to your back. Situps and hanging leg or knee raises are both potentially bad for your back, so be careful and pay attention to your body. Planks are quite safe. Bicycle crunches also. Mountain climbers. There are so many.

Rapid-Fire Obliques
Standing Ab Abuse
Lil' Bunches O' Crunches
Planks