The Collaborative International Dictionary of English v.0.48:

Rhapsodic \Rhap*sod"ic\, Rhapsodic \Rhap*sod"ic\, a. [Gr.
   "rapsw,diko`s: cf. F. rhapsodique.]
   Of or pertaining to rhapsody; consisting of rhapsody; hence,
   confused; unconnected. -- Rhap*sod"ic*al*ly, adv.
   [1913 Webster]

WordNet (r) 3.0 (2006):

rhapsodic
    adj 1: feeling great rapture or delight [syn: ecstatic,
           enraptured, rapturous, rapt, rhapsodic]

Moby Thesaurus II by Grady Ward, 1.0:

69 Moby Thesaurus words for "rhapsodic":
   Alcaic, Anacreontic, Castalian, Homeric, Hudibrastic, Pierian,
   Pindaric, Theocritean, bardic, blissful, bucolic,
   bursting with happiness, carried away, delighted, didactic,
   dithyrambic, dramatic, eclogic, ecstatic, effusive, elate, elated,
   elegiac, enchanted, enraptured, enravished, enthusiastic,
   entranced, epic, euphoric, exalted, exultant, flushed, freaked out,
   heroic, high, idyllic, imparadised, in ecstasies, in heaven,
   in paradise, in raptures, in seventh heaven, intoxicated, jubilant,
   mock-heroic, narrative, on cloud nine, orgasmic, overjoyed,
   overjoyful, pastoral, poetic, poetico-mystical,
   poetico-mythological, poetico-philosophic, poetlike, possessed,
   rapt, raptured, rapturous, ravished, rhapsodical, runic, sapphic,
   sent, skaldic, thrilled, transported