There are many people who think "Well, if you have nothing to hide, there's no harm in your data persisting." Many have come forward to argue the logic of exactly where such a perspective fails. All I want to add is a brief foray into some of the Torah that might be relevant to such a conversation.
We start off with the basics: HaShem sees everything. If everyone else can see what we do, won't that bring us more in line with the basic tenets of Torah belief? Some people have a hard time internalizing the idea that they can't hide from HaShem. If people couldn't hide from one another, it would be natural to understand what it means that HaShem would know everything about you. This seems like a good thing.
Hold on a second, we also say that הנסתרות לה' אלקינו ונגלות לנו ולבננו - The hidden things are God's alone, and the revealed things are for us and our children. So, potentially, there is such a thing as actions that are hidden from the world, meant to be judged only by HaShem. Often we will judge a situation or a person incorrectly because of insufficient information to accurately assess the situation. These situations can always occur. There's no way to prove that there isn't something that we don't know.
You might ask about a court system in light of this truth. The answer is that maintaining a court system is a mitzwah given by HaShem. Under certain circumstances we are commanded to carry out judgement and sentencing. Since it is God who gave us such a commandment, if we do so according to His will, he will only hold those judging accountable for what they could know, but not what they couldn't.
This actually touches on the next major point. Halachah applies to a person's knowledge, not to objective knowledge. A Sefer Torah is kosher if the letters appear to be whole. If, under a microscope, it turns out that there are breaks in a letter not visible to the human eye then the Torah is one hundred percent kosher. We see from this that too much knowledge might not be helpful, perhaps even harmful. (In actual fact, if someone sees what might be a problem with a letter in a Torah, one consults a child and asks them what letter it is, if they correctly identify the letter--then the Torah is 100% kosher. Halachah isn't concerned with objective perfection, only "close enough to be easily recognized".)
Finally, let's get to Teshuvah. Again, one might be tempted to say: If someone is really driven to do proper Teshuvah, having an accurate and thorough list of everything they've ever done wrong would be really useful in making sure they covered it all. [In fact, there are stories of people who went to the Arizal, and he would look into their souls and list for them all of their past misdeeds and then give them tikkunim to do in order to rectify their situation. (תולדות הארי)]
Still, Rebbe Nachman points out that one of the greatest gifts HaShem gave us is the ability to forget. Most of us would crumble under the burden of knowing everything we ever did wrong. Through forgetting we can wipe the sleight clean and start afresh. Serving HaShem in a way that may actually be possible for us, where we are right now. When we want to do Teshuvah, so HaShem reminds us little by little, each according to our ability to fix the errors of past.
Furthermore Teshuvah has a number of different levels. We might do teshuvah for all of our past appropriate to our current level; yet as we rise in our service of God, we might have the oppurtunity to perform a still deeper teshuvah. This selective, gradual remembering of the magnitude of our sins also allows the teshuvah process to be possible. (Not everyone can be like David HaMelech who said חטאתי לנגדי תמיד - my sins are always before me [ie. I've never let myself forget about them.])
In other words, there are certain situations and certain lessons that are made easier by perfect recall, but most of the time most of us will find a foggy recollection of the past far more palatable.