The Blessed Virgin Mary is sometimes this to Catholics. While they believe that She is very powerful and strong, having even Satan himself fear her, you can't possibly read about Her apparitions at Fatima without crying and wanting to spread devotion towards Her so that She may be loved. And then we find out that very few people actually listened to Her, thereby hindering her chances at having more children and bestowing graces upon them.
She also had to watch her son die a painful and humiliating death for something he was innocent of. She also grew up in poverty.
The first Nephi of The Book of Mormon. Chosen by God to retrieve the brass plates, his older cynical brothers, Laman and Lemuel several times berate him. After he does retrieve said plates, he sees a vision of the coming of Jesus, and the fall of his nation. When all is well and done, his father dies, leaving him to be the leader of his family. Obviously, because of their jaded views of their second younger brother, they try to kill him, forcing him to relocate and eventually have to face his brothers and his descendants.
Orpheus is the premier Woobie of Greek mythology (if not in fiction in general). If he expressed such sadness after his wife's death that even Hades wept for him.
Hephaestus needs a hug. Stable, hard-working guy who's horribly ugly, born crippled, kicked out of Mount Olympus, possibly by his own mother, married to the goddess of beauty who never cared about him.
Played straight in God of War 3. Even Kratos was disgusted by the Olympians' treatment of him and his "daughter."
Medea has a bit of this going on. She was a princess of a foreign country, and when Jason arrived to get the Golden Fleece, she fell in love with him and used her magic powers to help him accomplish his quest on the condition that he'd marry her. They wound up fleeing the country to escape her father's anger, and in a lot of stories Medea had to kill her brother to distract the king long enough for them to get away. Okay, all well and good. But fast-forward a few years, and now she's a foreigner alone in xenophobic Greece aside from her husband and two children, estranged from her family and friends, and her husband has just announced that he's leaving her to marry the (younger, prettier) princess of Corinth for political gain and oh, by the way, she's going to have to be exiled from the country now but Jason is totally going to try to let her come back to be his mistress. Medea was not pleased at all and poisoned the princess before fleeing the country... so the Corinthians killed her kids.
Some versions of Medusa are this in a nutshell. When you're punished by being made a gorgon because Poseidon couldn't keep it in his pants and raped you in the temple of Athena, let's just say you definitely deserve a hug, even if the hugger is likely to get poisoned or turned to stone for his or her trouble.
Let's not forget Ariadne. Some versions have Dionysus force Theseus to abandon her, while others claim he did it willingly. But either way, poor girl! On the other hand, her sister Phaedra had it maybe even worse...
And oh yeah, there's also Hercules. While we can understand that Hera hated Zeus's infidelity, it was really terrible how she persecuted Hercules like that. It's not like he could help that he was her husband's illegitimate son...
Osiris from Egyptian Mythology. The poor guy was tricked and murdered by his brother, and later had his corpse torn apart by him too.
One could argue that Jesus knew what he was getting into.