Why are thighs important? I know it sounds like a silly or weird question, but I'm serious.


  Genesis 24:2
  
  One day Abraham said to his oldest servant, the man in charge of his household, “Take an oath by putting your hand under my thigh.
  
  Genesis 47:29
  
  As the time of his death drew near, Jacob called for his son Joseph and said to him, “Please do me this favor. Put your hand under my thigh and swear that you will treat me with unfailing love by honoring this last request: Do not bury me in Egypt.
  
  Leviticus 7:33
  
  The right thigh must always be given to the priest who offers the blood and the fat of the peace offering.
  
  Revelation 19:16
  
  On his robe at his thigh was written this title: King of all kings and Lord of all >lords.


Why is the thigh important?
The usages you give here are varied and not necessarily related. In today's English would could use the word hand as in to 'offer a helping hand' or to 'hand something over' or 'hand something out' or any number of other expressions. In the same way not every instance of the word 'thigh' necessarily refers to the same thing.

The first two cases you give in Genesis have to do with oaths. Placing a hand on the thigh of someone while you made a promise was a sign of submission and the seriousness of the oath. Such an action could also be taken on ones self as a sign of remorse. There several other examples of these two usages throughout the OT.

In your Leviticus passage the meaning is entirely different and you need look no farther than the prices of different cuts in your local butchers shop for an explanation. Some cuts of meat are considered more valuable. Breast and thighs were considered the best portions.

I don't know what the significance in Revelation is. For this one the suggestion to ask on Judaism.SE might be a good one because It think it has to do with a specific piece of clothing, the Tallit. The tassels have significance and where on the garment the name is inscribed corresponds to something about the tassels.