#LONG implies a wishing with one's whole heart and often a striving to attain. E.g., He longed for some rest after his final exams.
#YEARN suggests an eager, restless, or painful longing. E.g., I have been yearning for a stage career in New York.
#HANKER suggests the uneasy promptings of unsatisfied appetite or desire. Those who always hanker for money will never satisfy, no matter how much money they earn.
#PINE implies a languishing or a fruitless longing for what is impossible. E.g., Men always pine for their lost love.
#HUNGER and #THIRST imply an insistent or impatient craving or a compelling need. E.g., Albert hungered for a business of his own; Frank Underwood thirsted for power even though he was supposed to lose the reelection.