4 Answers

Synonyms for "inspire" are:
exhilarate,
invigorate,
galvanize,
influence,
motivate,
occasion, and
reassure!!!

I agree with lindilou's answer.  Just wanted to add that "being inspired" is motivation with sustainability.  Hence, try to be inspired, not motivated.  For example, be inspired to be a good father, and get motivated to keep the house clean right before your in-laws arrive from Illinois.

ignite 

stimulate

affect, animate, arouse, be responsible for, carry, cause, commove, elate, embolden, endue, enkindle, enliven, exalt, excite, exhilarate, fire up, galvanize, get*, give impetus, give one an idea, give rise to, hearten, imbue, impress, infect, inflame, influence, inform, infuse, inspirit, instill, invigorate, motivate, occasion, produce, provoke, quicken, reassure, set up, spark, spur, start off, stir, strike, sway, touch, trigger, urge, work up