Can I play on whatever server I want?

After Diablo 3 has officially launched in all regions, you will be able to play on any server you want. However, characters and items will not transfer over.

As per the Launch Day Preparation Guide:

We’ll be turning on Global Play when the game has launched in all regions. This means that you will not be able to play in a region outside your home region until after the Americas’ midnight launch at 12:01 a.m. PDT on May 15. We’ll provide an update once Global Play is enabled, and you’ll then be able to change the region you connect to through the game’s options. Please note that characters, items, and friends lists do not transfer across regions and players who use Global Play to connect outside of their home region will only be able to access the gold-based auction house. More information can be found in our Global Play introduction article.