As Dave stated, no shorts are allowed for dinner in the main dining room(s). If you plan on wearing shorts you will have to go to the Windjammer for dinner. On casual nights, I usually wear khakis and a button down shirt, no tie or jacket.
On formal nights, I wear dress slacks, a shirt and tie, and jacket.
2007 - Majesty of the Seas
2009 - Enchantment of the Seas
2010 - Freedom of the Seas
Christineken, there will be people who will wear "nice" shorts to dinner and it's rare that they are turned away. It's frowned upon and sometimes the rules are actually enforced. As cruise enthusiasts, we follow the rules of dinner etiquette and will not allow anyone to tell you that it is ok to wear shorts to the dining room.