The Collaborative International Dictionary of English v.0.48:

Self-importance \Self`-im*por"tance\, n.
   An exaggerated estimate of one's own importance or merit,
   esp. as manifested by the conduct or manners; self-conceit.
   [1913 Webster]

WordNet (r) 3.0 (2006):

self-importance
    n 1: an inflated feeling of pride in your superiority to others
         [syn: ego, egotism, self-importance]
    2: an exaggerated opinion of your own importance [syn:
       egotism, self-importance, swelled head]