Every year, someone asks the relevent question, "How on Earth did a custom of hunting for dyed hard-boiled eggs left by a rabbit develop anyway?" And I have never been able to answer this question. I'm aware that the word 'Easter' in English derives from the Anglo-Saxon fertility goddess Eostre, and that rabbits and eggs were both symbols of fecundity in pre-Christian Europe, but still, rabbits that laid brightly colored eggs seem like a long stretch.
So, God bless Google, I've done some hunting this year. Per InfoPlease, I've got a few interesting details:
First, Lent. I hadn't made this connection, but since eggs were considered meat during Lent in medieval times, eggs laid during this time were boiled or otherwise preserved, and served in quantities at Easter, as soon as they could be eaten. (Note: during the Middle Ages, the Lent fast from meat was ALL of Lent, not just Fridays, and what they reckoned as meat was pretty all-inclusive.)
Decorating eggs for the Easter holiday in a variety of ways seems to be a tradition spread across Europe throughout the Middle Ages. Apparently it was the Germans, though, who developed a tradition of the 'Easter hare', who hid eggs for children to find, and brought the custom of the Easter egg hunt to America. They may have also developed the chocolate egg.
Per homecooking.com, in some parts of Europe, children go door-to-door, Halloween style, to ask for Easter eggs.
OK, but I'm still asking myself, why would a rabbit, or a hare, be interested in bringing small children hard-boiled eggs? Checking with Wikipedia, I get this:
The idea of an egg-laying bunny came to the United States in the 18th century. German immigrants in the Pennsylvania Dutch area told their children about the "Osterhas," sometimes spelled "Oschter Haws." "Hase" means "hare," not rabbit, and in Northwest European folklore the "Easter Bunny" indeed is a hare, not a rabbit. According to the legend, only good children received gifts of colored eggs in the nests that they made in their caps and bonnets before Easter. In 1883, Jakob Grimm wrote of long-standing similar myths in Germany itself. Noting many related landmarks and customs, Grimm suggested that these derived from legends of Ostara.
The German and Amish legends were most likely rooted in European folklore about hares' eggs  which seems to have been a confusion between hares raising their young at ground level and the finding of plovers' nests nearby, abandoned by the adult birds to distract predators. Hares use a hollow called a form rather than a burrow. Lapwings nest on the same sort of ground, and their nests look very similar to hare forms. So in the Spring, eggs would be found in what looked like hare forms, giving rise to the belief that the hare laid eggs in the spring.
OK. For a really charming children's version of all of this, may I recommend The Country Bunny, and the Little Gold Shoes?