I've always known the right hand as being the hand of strength and power intuitively. Anyway, I've checked the Easton's Bible Dictionary and there are many references where the right hand is used:
You can read up the references. There is also a custom among the Israelites to pronounce blessings on their children just before they pass away. We see this in action in the following scripture [Genesis 48:13-19]. Israel took Joseph's two sons, Manasseh (the first-born) and Ephraim (the second son) as his own children and blessed them. Israel was then very old and could not see clearly but he did a prophetic act. When Joseph brought his two sons, he placed Manasseh on Israel's right hand and Ephraim on Israel's left hand. In a prophetic act, Israel crossed his hand and placed his right hand on Ephraim and his left hand on Manasseh. Because of this act, Ephraim received a double portion of the blessings. There is apparently from this tradition greater emphasis in terms of power and strength and blessings on the right hand.
I don't really know why the right hand is used but we see the right hand and sitting at the right hand in many scripture references.