The Collaborative International Dictionary of English v.0.48:

Aspire \As*pire"\, v. i. [imp. & p. p. Aspired; p. pr. & vb.
   n. Aspiring.] [F. aspirer, L. aspirare. See Aspirate, v.
   t.]
   1. To desire with eagerness; to seek to attain something high
      or great; to pant; to long; -- followed by to or after,
      and rarely by at; as, to aspire to a crown; to aspire
      after immorality.
      [1913 Webster]

            Aspiring to be gods, if angels fell;
            Aspiring to be angels, men rebel.     --Pope.
      [1913 Webster]

   2. To rise; to ascend; to tower; to soar.
      [1913 Webster]

            My own breath still foments the fire,
            Which flames as high as fancy can aspire. --Waller.
      [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

Aspiring \As*pir"ing\, a.
   That aspires; as, an Aspiring mind. -- As*pir"ing*ly, adv.
   -- As*pir"ing*ness, n.
   [1913 Webster]

WordNet (r) 3.0 (2006):

aspiring
    adj 1: desiring or striving for recognition or advancement [syn:
           aspirant, aspiring(a), wishful]