They can be dangerous
If you do the right crunches, they can be harmless but most of the people are not doing them right. If you want to do crunches in a safe and effective manner, you will need lots of body awareness and anatomical knowledge. There are some people who throw their legs in the air or add some twists while performing crunches. While performing crunches, you can pull a muscle, sleep some this in your spine and make create other health problems which may not show up immediately but they may appear at a later time.
Not so good for your spine
Regular crunches are not good for your spine and they can wreck havoc on your spine. Good instructors will tell you to flatten your spine to the floor when you do crunches. It can protect you from major injury to some degree but while doing that, you may also train your body to stay in that flattened position. Your spine naturally has curves for a reason. Good core training will take into account those curves and accordingly train your body to move. They will also support your spine without having to compromise a natural integrity of its form. But doing simple crunches may not worry about the natural curves or your spine and that can create big problems.
If you release the spine too much while performing crunches or overextend the curve of the lower back, it can result in major issues for your spine and this is something that you don't want.
May result in poor posture
If you are performing crunches regularly and if you are not doing it right, it can result in poor posture. Many people tuck their butt under and hold in their abs because they have done too much bad crunches. This is bad for you because it disrupts the natural curves of the spine. At the end, regular crunches can result in strong bad posture.
Your whole body is a connected system and if you are tucking bottoms it can result in spinal curves which may slump your shoulders downward, the head forward. It can also result in old lady hump and cause a poor posture that you don't want.
Crunches mostly focus on the surface muscle but they do not focus on the deep core muscles and this is a mistake. If you're over focusing on surface muscles instead of deep core muscles, you will not get the six-pack abs or other well-defined look of your abs, for which you are performing the crunches. Crunches zone your surface ab muscles. If you want strong core, you need to focus on the through core strength and crunches do not work on those core muscles. If you're only concerned about how your stomach looks, then you can go ahead and do crunches but if you want real strength in your core which will support the body in motion, you'll have to go deeper and focus on the deep core muscles.
Tension and restriction of the hips
When you perform crunches regularly and you tuck your butt under while performing it, it will overwork surface muscles but will disengage more core muscles. It will tighten hip flexors and will create tension in the hips. It can result in problems in the hip joint which may cause lower back pain.