General longing:
* Desire
* Crave
* Long for
* Pine for
* Wish
* Hanker
* Yearn after
Strong, intense longing:
* Ache for
* Burn for
* Languish for
* Throb for
* Yearn passionately
Yearning for something lost or unattainable:
* Mourn
* Regret
* Wistful
* Nostalgia
* Melancholy
Yearning for connection or love:
* Love
* Adore
* Worship
* Cherish
* Embrace
* Miss
Other synonyms:
* Aspire
* Seek
* Hope
* Dream
The best synonym to use will depend on the specific context and the emotion you are trying to convey.