Can We See God?

Today I was reading in John 14 when something at the end of verse 21 caught my attention.

"He that hath my commandments, and keepeth them, he it is that loveth me: and he that loveth me shall be loved of my Father, and I will love him, and will manifest myself to him."  I read this and asked myself the question, "Can we see God?"  I remembered several scriptures about some prophets that had seen Him and decided there must be some requirements.  Here are some of the scriptures that I looked up:

I have seen God face to face, Gen. 32:30
Moses … was afraid to look upon God, Ex. 3:6
Lord will come down in the sight of all the people, Ex. 19:11
nobles of the children of Israel … saw God, Ex. 24:11
Lord spake unto Moses face to face, Ex. 33:11

I will love him, and will manifest myself to him, John 14:21 

I see … the Son of man standing on the right hand, Acts 7:56 

etc.   (for the complete list: God, Privilege of Seeing)

One that stuck out to me was in Matthew 5:8  which says, "Blessed are the pure in heart: for they shall see God."  I had read this scripture many times, but never really thought about what it meant.  Jesus is giving the Sermon on the Mount and tells us that we can see God if we are pure in heart.  So what does 'pure in heart' mean?
D&C 67:10 says "that inasmuch as you strip yourselves from jealousies and fears, and humble yourselves before me, for ye are not sufficiently humble, the veil shall be rent and you shall see me and know that I am—not with the carnal neither natural mind, but with the spiritual."  This tells me that we need to not be jealous, fearful, or prideful if we are to have the opportunity to see God the Father.  I looked up some other references and found James 4:8 which says to "Draw nigh to God, and he will draw nigh to you. Cleanse your hands, ye sinners; and purify your hearts..."  So as long as we are drawing unto God, and cleansing our hands, we are purifying our hearts.  This reminded me of another scripture in Revelation 3:20 which says, "Behold, I stand at the door, and knock: if any man hear my voice, and open the door, I will come in to him, and will sup with him, and he with me."  
In conclusion, I believe that we need to draw closer to God.  As we do this by avoiding the carnal mind and humbling ourselves, we can be 'pure in heart'  This includes virtuous thoughts, words, and actions.  As we do these things, we are promised in the scriptures that we will see God.