The answer by @Skooba covers the majority of these cases but I can think of a few more.
Maegor "The Cruel" Targaryen
Although it is unknown how exactly he died common belief is that he commited suicide.
Maegor's response to this was slow and confused, and it seems that this series of betrayals—and perhaps even the loss of his mother's guidance—had left him, in his own way, as broken as Aenys. He called his loyal lords to King's Landing, but all that came were minor lords of the crownlands, who had little to marshal against the king's many enemies. It was late at night, during the hour of the wolf, when the remaining lords departed the council chamber, leaving Maegor to brood alone. Early the next morning, he was found dead on the throne, his robes sodden with blood, his arms slashed open by the barbs of the Iron Throne.
Thus ended Maegor the Cruel. How he came to die is a matter of much speculation. Though the singers would have us believe that the Iron Throne itself killed him, some suspect his Kingsguard, and others some mason whom the king had failed to kill and who knew the secrets of the Red Keep. But perhaps even likelier is the suggestion that the king killed himself rather than suffer defeat. Whatever the truth, it was a reign that ended in the only way it could after the six years of terror that Maegor had visited upon the realm. But his nephew's reign would do much to mend the deep wounds he had made in the Seven Kingdoms.
The World of Ice and Fire, The Targaryen Kings: Maegor I
Although not technically suicide he persuades Jon to kill him to win favour from the wildlings.
"I've told you the truth. Our garrons were failing, and Rattleshirt was close behind us. Qhorin told me to pretend to join the wildlings. 'You must not balk, whatever is asked of you,' he said. He knew they would make me kill him. Rattleshirt was going to kill him anyway, he knew that too."
A Storm of Swords, Jon IX
House of Black and White Visitors
Many people come to the House of Black and White to be given the gift and drink poison from the fountain.
Sky cell prisoners
Tyrion's arms were too short to reach the plate, and he was not about to step that close to the edge. All it would take would be a quick shove of Mord's heavy white belly, and he would end up a sickening red splotch on the stones of Sky, like so many other prisoners of the Eyrie over the centuries. "Come to think on it, I'm not hungry after all," he declared, retreating to the corner of his cell.
A Game of Thrones, Tyrion V