When we go to heaven will we remember our life on Earth?

The Bible gives us strong assurance that we will retain memories of our life on earth, at least to a degree, as well as our personalities and the degree of spiritual maturity we obtain while on earth.

First, we know that we will retain our identities, at least in the sense of our unique personalities. For example, the Lord promised that the 12 Apostles would rule over the 12 tribes of Israel in the Kingdom:

Matt. 19:27  Then Peter said to Him, “Behold, we have left everything and followed You; what then will there be for us?” 
Matt. 19:28 And Jesus said to them, “Truly I say to you, that you who have followed Me, in the regeneration when the Son of Man will sit on His glorious throne, you also shall sit upon twelve thrones, judging the twelve tribes of Israel."

Obviously, if these men receive what has been promised to them, they maintain their identities, and if they maintain identities, then they must retain memories, for our identity is the result of a lifetime of experiences. 

Likewise, the Bible promises that King David will be resurrected and reign over Israel in the Kingdom (though still under Christ's authority as King of the world). Speaking of the Millennial Kingdom, Ezekiel says:

Ezek. 37:24  “My servant David will be king over them, and they will all have one shepherd; and they will walk in My ordinances and keep My statutes and observe them. 
Ezek. 37:25 “They will live on the land that I gave to Jacob My servant, in which your fathers lived; and they will live on it, they, and their sons and their sons’ sons, forever; and David My servant will be their prince forever." 

David must maintain his identity (and memories) after the resurrection in order for God to fulfill this prophecy. When we enter the Kingdom, we will all know David as David, which means both David and everyone else must retain memories of life on earth. We must know each other as who we were on earth originally, otherwise this promise to David would be meaningless. So, we can safely conclude we must maintain some degree of memory in the Kingdom. 

We also retain our degree of spiritual maturity gained on earth. The Lord promises that those who are faithful with little in this lifetime will be counted worthy for greater responsibility in the age to come:

Luke 16:9 “And I say to you, make friends for yourselves by means of the wealth of unrighteousness, so that when it fails, they will receive you into the eternal dwellings.
Luke 16:10  “He who is faithful in a very little thing is faithful also in much; and he who is unrighteous in a very little thing is unrighteous also in much.
Luke 16:11 “Therefore if you have not been faithful in the use of unrighteous wealth, who will entrust the true riches to you?"

Notice that Jesus says we are to use our time (and money) now to further the purposes of the Kingdom, so that when we enter the Kingdom we will be welcomed by friends who remember our generosity. Clearly, we must maintain some degree of memory after our resurrection if Jesus’ words are to be understood literally. 

Furthermore, the Lord tells Israel that they will remember their sins against the Lord when they enter the Kingdom:

Ezek. 20:39  “As for you, O house of Israel,” thus says the Lord GOD, “Go, serve everyone his idols; but later you will surely listen to Me, and My holy name you will profane no longer with your gifts and with your idols.
Ezek. 20:40 “For on My holy mountain, on the high mountain of Israel,” declares the Lord GOD, “there the whole house of Israel, all of them, will serve Me in the land; there I will accept them and there I will seek your contributions and the choicest of your gifts, with all your holy things.
Ezek. 20:41 “As a soothing aroma I will accept you when I bring you out from the peoples and gather you from the lands where you are scattered; and I will prove Myself holy among you in the sight of the nations.
Ezek. 20:42 “And you will know that I am the LORD, when I bring you into the land of Israel, into the land which I swore to give to your forefathers.
Ezek. 20:43 “There you will remember your ways and all your deeds with which you have defiled yourselves; and you will loathe yourselves in your own sight for all the evil things that you have done.
Ezek. 20:44 “Then you will know that I am the LORD when I have dealt with you for My name’s sake, not according to your evil ways or according to your corrupt deeds, O house of Israel,” declares the Lord GOD.’”

The Lord says plainly that the nation, having been resurrected and glorified in the Kingdom to come, will remember its sins against Him and "loathe" themselves for having done so much to offend God. The word loathe is a particularly strong word in Hebrew, and it clearly indicates we will possess negative memories.

Moreover, the Lord says the reason such memories exist is so that we can fully appreciate His grace. Notice in v.44 the Lord says that the effect of memory will be to magnify His mercy and grace for having dealt with Israel NOT according to their deeds. In other words, God did not punish them as He should but rather showed Israel grace. 

Having a memory of our past life will be important to appreciate the grace of God extended to us in Christ. After all, how could we celebrate the Lord for His grace and mercy shown to us if we can't remember what we were forgiven for? On the other hand, the scriptures also indicate that the mistakes of our life of earth will not diminish our joy once we reach the New Heavens and New Earth.

For example, the Bible says:

Rev. 21:3 And I heard a loud voice from the throne, saying, “Behold, the tabernacle of God is among men, and He will dwell among them, and they shall be His people, and God Himself will be among them, 
Rev. 21:4 and He will wipe away every tear from their eyes; and there will no longer be any death; there will no longer be any mourning, or crying, or pain; the first things have passed away.” 

Perhaps we will remember past disappointments yet without sorrow. Nevertheless, we can say that though memories persist into Heaven, sadness and mourning do not.