The abdominal muscles flex your spine or, in other words, bring your bottom rib closer to the top of your pelvis. Anything that stresses and strengthens these muscles is considered an ab exercise.
Holding good posture--or anything that forces your muscles to keep your torso properly aligned--is an isometric ab exercise. Get the most out of this by challenging yourself to hold good posture in difficult positions, such as the plank position.
Being able to do ab exercises with no equipment means that you can strengthen your core almost anywhere, at any time, that you desire. It also saves the money that you might otherwise have spent on ab equipment.
In order to strengthen your abdominals quickly, you must overload them or make them do more work than they're used to doing, without adding so much stress to them that the muscles become injured.
Since you're not using equipment to provide extra resistance against and challenge for your ab muscles, you'll need to use gravity--plus the weight of your own body--instead.
One of the best ways to challenge your abs with no equipment is to use leverage; try extending your arms directly your head, as far from your hips as possible, when doing crunches. The added lever length makes the exercise much more challenging.