5) Captured, tortured, executed. This has a good chance of happening, but is my least favourite. His army loses on the field of battle, he is captured, then brutally tortured, and finally executed. In this scenario, Sansa Stark will almost certainly be on the winning side and help decide how he'll meet his end.
4) Killed during sex. Likely with a prostitute or a peasant girl who works for the Bolton's in Winterfell. During some act of depravity, he gets killed when he least expects it. He could be tied up on the bed with a ball-gag in his mouth, attached to some weird trapeze, or plain and simple rape; then suddenly a knife in the chest.
3) Killed in combat with Brienne of Tarth. There are a few different paths that could logically lead to this outcome, whether it is in a battle, assassination, or even trial by combat. Certainly if any set of circumstances puts Brienne anywhere near Ramsay, his life is in danger.
2) Killed by his own dogs. It would be pretty awesome if Bran mind controlled Ramsay's dogs and ripped him to pieces. Fans would love to see this happen, but it is still not the most entertaining possibility. It would be a fitting end, all things considered.
*NOTE* A few weeks after writing this post, Ramsay was mauled to death by his own dogs. I had hoped that Bran would be mind controlling the dogs at the time, but that part was wrong. It was a fantastic episode of the show, but could have been even better if...
1) Absorbed by the army of the dead. This would be the most fun to watch. He marches his army North attempting to consolidate his control, and ends up meeting the White Walkers and the army of the dead in another Hardhome type massacre. The look of terror on his face would be truly priceless.