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ZenithNadir Dragon eggs are not capable of hatching until at least two days have passed. During that time you have to monitor your eggs to make sure they're getting sufficient views.
BUT. The speed at which you get views has an impact on gameplay.
Not getting enough views is basically what happens when your egg reaches a point in which it is capable of hatching but hasn't yet (a little more than 4 days left before it will die). If your egg reaches 4 days left and hasn't hatched, it becomes eligible for an emergency room in a click site. It triggers an auto-refresh function that is quicker than the other eggs/hatchlings that don't have emergency status. In short, it speeds up the views your egg gets and makes it hatch before its too late. It's an egg saver. xD I'll post links to click sites for you.
HOWEVER...
The worst case scenario is ironically a situation in which your eggs get clicks/views
too quickly. This results in a disease that players have unofficially named Softshell. The game will alert you when one or more of your eggs gets sick, and when they do, you have to act quickly. You have to click on your egg's Actions tab, select Hide, and wait until the disease goes away. When an egg is under the effects of Hide, its sprite turns into a little foggy cloud. This makes it so it wont get any views until the egg is unhidden.
Eggs require a certain views/clicks/time left ratio to hatch, but that ratio seems to be different for every egg. Sometimes eggs wont hatch until they get 5,000 views, 700 unique views, and 10 clicks. Another egg might hatch with only 2,000 views, 300 unique views, and 8 clicks. The system for predicting the views needed has not been discovered, which adds some excitement to the game. :)
My tip to avoid complications: Don't add your eggs to click sites too quickly. The first day you can maybe put your eggs in one click site, then the next day you can add them to another, etc.
There is so much more to say about the game though, because for its simple interface Dragon Cave is actually a very detailed game. It has a LOT of secrets.
Click sites:
http://greg-kennedy.com/dragcave/
http://valleysherwood.com/
http://www.allureofnds.net/ (I highly recommend this one)