1) Ache 2) Desire 3) Discontentedness 4) Discontentment 5) Eager 6) Hankering 7) Homesick 8) Homesickness 9) Infatuated 10) Itch 11) Nostalgia 12) Nostalgic 13) Pensive 14) Pining 15) Repining 16) Thirst 17) Wish 18) Wishfulness 19) Wistfulness 20) Yearning 21) Yen 1) Appetite 2) Desire 3) Eager desire 4) Hankering 5) Hunger 6) Passion 7) Play by William Boyd 8) Thirst 9) Yearning 
• (p. pr. & vb. n.) of Long • (n.) An eager desire; a craving; a morbid appetite; an earnest wish; an aspiration.
Long'ing noun An eager desire; a craving; a morbid appetite; an earnest wish; an aspiration. « Put on my crown; I have immortal longings in me.» Shak. 
[n] - prolonged unfulfilled desire or need
yearning noun prolonged unfulfilled desire or need
strong, persistent desire or craving, esp. for something unattainable or distant: filled with longing for home. · an instance of this: a sudden longing to see old friends.