Appear, Look & Seem

APPEAR
1. Give the impression of being.   
            They do not appear to be at home.
2. It can also mean 'arrive' but in this case can be modified by an adverb.  
             She suddenly appeared in the doorway.  
                         
LOOK        

Have the appearance or give the impression of being. 

            He looks like his mother.
            He looks tired.

SEEM            
Give the impression of being something or having a particular quality.
          It seems like Bill is falling in love with Smantha.
seems like -- indicates a possibillity of something

         It seems that Bill is falling in love with Smantha.
seem that --- indicates a more factual situation  
                                                                                          Wordreference