WARNING: Spoilers abound throughout the text. If you don't want to know, stop reading now.
The explosive season finale of Game of Thrones saw Cersei Lannister ascend to the Iron Throne. But did the writers give away -- or at least, give a strong hint to -- the answer to another question lingering since Season 4: Who gave Gregor Clegane -- aka the Mountain -- the order to rape and murder Elia Martell?
Oberyn Martell -- aka the Red Viper of Dorne -- offered to fight for Tyrion Lannister in his trial by combat for charges of regicide. Martell's motive for doing so is made clear once his fight with Clegane begins. He wants Clegane to confess to raping and murdering his sister Elia, and murdering her children, and he wants to know who gave him the order. Though Oberyn Martell directs his accusations during the fight toward Tywin Lannister, the likely culprit behind Elia's death is Cersei Lannister.
First, in the recent season finale, Cersei has a key scene with her former tormentor Septa Unella, who is restrained on a rack while being waterboarded with wine. At the end of their conversation, Cersei calls in the now-zombified Gregor Clegane to (presumably) rape or torture or kill (or possibly all three) Septa Unella behind closed doors. If she had no problem unleashing the Mountain on a defenseless woman in the present, what's to say she hasn't already done it before?
The second bit of evidence is from Cersei's own history. Some back story is necessary for context: before the series began, the Targaryen family ruled the Seven Kingdoms, with Aerys II sitting on the Iron Throne. His son Prince Rhaegar was married to Elia Martell. When Rhaegar kidnapped Lyanna Stark -- sister of Ned Stark, he set in motion Robert's Rebellion, a civil war which resulted in the overthrow of the Targaryen family and the death of most of its members.
In the books, Cersei was originally meant to be betrothed to Rhaegar Targaryen, an offer that was turned down by Aerys II. Once the Lannisters turned against the Targaryen family and the Sack of King's Landing was underway, the Lannisters, along with their Baratheon allies, wanted to end the Targaryen dynasty and kill as many of them as possible. The motive remains unknown for now, but if she felt jilted or betrayed because her betrothal to Rhaegar never happened, perhaps she decided to take revenge on his wife. Cersei was later betrothed to Robert Baratheon, the new king. Consequently, they probably didn't want any Targaryens disputing their children's claim to the Iron Throne, which is probably another reason Cersei would have wanted Elia Martell and her children dead.
Subsequent events show that the Lannisters and the Baratheons failed to exterminate the Targaryen line: First, Rhaella, Aerys's queen, fled King's Landing with a young Viserys while pregnant with her daughter Daenerys. Second, as revealed in the recent season finale, the seemingly official confirmation of the longstanding R + L = J theory, which states that Jon Snow is the son of Rhaegar Targaryen and Lyanna Stark.
This is pure speculation, so we probably won't know more until the next book comes out or the start of Season 7 (probably the latter). But the circumstantial evidence is suggestive of Cersei Lannister's complicity.