Thranduil, as portrayed by Lee Pace
Thranduil is King of Mirkwood and the father of Legolas. He appears in The Hobbit, but is alluded to in Lord of the Rings. More information about him appears in Unfinished Tales. He comes across as stern but fair.
In Badfic
Some people who have read The Hobbit think badly of him for imprisoning Thorin's party in his dungeons, as well as a stated love of treasure. This disregards the fact that the latter wasn't enough to prevent him from lending aid to the Lake-men on the way to Erebor, and that the former was partly caused by Thorin and the dwarves' rude behavior (in which they showed less respect to him than they did to the Goblin King). Not only that, but the Elven fondness for wine featured in the book is used as grounds for pegging Thranduil as an alcoholic, and therefore physically abusive.
This last characterization has become popular in large sections of the fanfic community as fans seek new ways to woobify Legolas. Not merely that, but many authors add rape and incest into the mix, despite the fact that there is no evidence at all that Thranduil ever mistreated Legolas. Fics like this also have the latter as a little kid, even though logically, he would be centuries old in the time period most authors set Abusive!Thranduil fics in. Thankfully, there is hope of this trend fading with the coming of the new Hobbit movie trilogy. In fact, the Hobbit films have given rise to the fandom interpretation of Thranduil as a "racist party dad", frequently seen dancing to strobe lights, braiding other elves' hair, wearing shutter glasses, and hating Dwarves. The infamous moose/elk thing also makes an appearance.
Other fics have his evil restricted to him forbidding Legolas from marrying whichever Mary Sue catches his eye (this is actually a good thing) or arranging marriages to other Mary Sues from Lorien, Rivendell, or a made-up kingdom of elves (this, however, is bad). Sometimes, he is cast as homophobic in order to provide an enemy to the Aragorn/Legolas ship. Other slash fics have him ignore the Ranger and the Elf's relationship, or even encourage it. (Though it may be useful to note that these can be done well in a plausible AU in which 'The Laws and Customs of the Eldar' do not apply.)
ManyPPC Agents have a soft spot for Thranduil simply because of the aforementioned characterisations.
External Links
Thranduil at Tolkien Gateway
Thranduil at Lotr.wikia
In Defense of the Elvenking, by Karri
A Case of Mistaken Identity, by Conquistadora