Just a note-- apparently there are special "Valentine's Day" eggs today. Possibly only today-- I'm not sure. They look like this:
I haven't been able to spot one in the cave or the main page, and I'm full up anyway, so I couldn't pick one up even if I wanted to.
Maybe one of my existing eggs will hatch before there aren't any more of these, or maybe not.
Edit: If you're at the Dragon Cave page looking for these, the description is "This egg is speckled and very fragile." There's a limit of 2 per person. It's not clear yet if the grown-up dragons will be able to breed or not.