In edit mode I can press W to bring up the specials menu, then D to shade smooth. Is there any shortcut key for shade smooth in object mode? I know I can assign a key, but wanted to know if there already is one in blender.
No. There is not.
There are two good places to look for shortcuts. The Space menu, and the user preferences.
If there were shortcuts, they would show up there:
You can set hotkeys like shown in this example: