May also precedes the full-fledged tourism season when all the university students on summer break grab their backpacks, fill up the hostels and trains, and flood the streets of Europe. Thus you might even be able to find a (relatively) cheap flight.
Also, there's just something about Spring in Europe. Fall (formerly my favorite season) is a little bit of a let-down here - it doesn't have the pumpkin everything, apple cider, donuts, and the fabulous displays of foliage like North America. But spring.... ahhh spring. Europe is the place to be. It is the continent of sidewalk cafes and people-watching. And even if there's still a bite in the air, people will sit outside at bistro tables, wrapped in a thin blanket if necessary, drinking their cappuccinos and espressos (and yes, smoking), and just lingering all afternoon. The beer gardens and parks start to fill up, cyclists are everywhere, and lush flower displays start to brighten up window boxes and city streets.
One of the things that I love most about Bavaria at this time of year are the exuberant yellow fields of grapeseed flowers. They are everywhere outside the city, along all the highways and minor byways, and are vast, thick blankets of yellow flowers. A cycling trip through these fields should be on the agenda sometime soon...
So May is the time I beseech you to visit.
But now that I think about it, May is only a good time to come to Germany if you are visiting someone. Otherwise, it is the most annoying month for a traveler, because you have to constantly contend with the public holidays... your mantra will become: "why did nobody tell me all the stores would be closed on a Thursday?! Again? What the hell?!"