Adam and Eve were naked, and they were not ashamed (Gen 2:25). The Hebrew word for naked Arowm here means nude, naked nothing more or less.
There was no need to be ashamed of their nakedness, there was no need for clothing as a form of protection.

What does the bible say about nudity?
All Bible passages are taken from the King James version because it closest to the original text and it's on my computer, it's easier to copy and paste – yeah, I'm lazy.

Gen 1:26 And God said, Let us make man in our image, after our likeness.......

Leviticus 18:6
6 None of you shall approach to any that is near of kin to him, to uncover their nakedness(Ervah): I am the Lord.

1 Sam 19:24
And he stripped off his clothes also, and prophesied before Samuel in like manner, and lay down naked (Arowm) all that day and all that night. Wherefore they say, Is Saul also among the prophets?

Isaiah 20:2-3
2 At the same time spake the Lord by Isaiah the son of Amoz, saying, Go and loose the sackcloth from off thy loins, and put off thy shoe from thy foot. And he did so, walking naked and barefoot.
3 And the Lord said, Like as my servant Isaiah hath walked naked (Arowm) and barefoot three years for a sign

New Testament:
John 21:7 Therefore that disciple whom Jesus loved saith unto Peter, It is the Lord. Now when Simon Peter heard that it was the Lord, he girt his fisher's coat unto him, (for he was naked; gumnoss,) and did cast himself into the sea.

Romans 6:11-14
11 Likewise reckon ye also yourselves to be dead indeed unto sin, but alive unto God through Jesus Christ our Lord. 12 Let not sin therefore reign in your mortal body, that ye should obey it in the lusts thereof. 13 Neither yield ye your members as instruments of unrighteousness unto sin: but yield yourselves unto God, as those that are alive from the dead, and your members as instruments of righteousness unto God. 14 For sin shall not have dominion over you: for ye are not under the law, but under grace

There are many other places in the bible where nudity is mentioned. I have listed just a few for the purpose of this essay.

The essay;
What is our problem with being nude?
Why do we have such a fear of it?
I think it stems from the garden of Eden. After the bite, Adam and Eve lost their innocence.

Adam and Eve sinned. They defied the law of God. Their nakedness became a symbol of the purity they once knew, it shamed them, and in an effort hide from that purity, they tried to cover it by making aprons for themselves made of fig leaves (Gen 3:7).
When God created Adam and Eve, He created them nude, as they should be naturally. Like every other creature, their bodies needed no more covering than they had been given.
Adam and Eve weren't trying to cover themselves in an attempt to hide their nakedness for sexual reasons, nor were they afraid of what the other might think(Gen 3:7). They tried to hide from themselves by covering their bodies, and then, when God arrived in the cool of the day, they tried to hide from Him too(Gen 3:8-10).
They knew they had done wrong, their new found knowledge of good and evil had nothing to do with their naked state. They were ashamed of what they had done, disobeyed God, not of being naked.
Being nude per se wasn't wrong, that is the way God created them, (Gen 2:25 they were naked and they were not ashamed).
Of course the big question is; Why did God give his children garments made from the skin of a dead animal?
One understands that an animal had to die for their sin, there needed to be a sacrifice to atone for the sin, but why use the skin for garments?
Was it because God knew they would need clothing to protect themselves from the harsh environment they were about to enter, or was it for another reason?
If it was for protection, then why not use a fabric made from plants?
Or, was it because of what they had done?
Had God decided to cover the purity of their innocent nakedness with animal skins, skins of creatures lower than themselves, to teach them a lesson, or show them how far they had strayed from Him?
Perhaps this is the very reason why we are now hard wired to the need for clothing, to keep ourselves covered, lest we be shamed by our own nakedness.

As you can see, the above Bible passages show that no where, in the Bible does God condemn nudity either in public or private.
The naked body is not shameful, but what we do with it can be.
It is shameful to gaze upon the nakedness of someone without their consent, it is shameful to have sexual thoughts of someone you are not married to.
See 2 Sam 11:2. It was not wrong for the woman to wash herself in her home, the passage implies that she was nude (one needs to be nude to bathe I believe she didn't know David could see her).
Isaiah was nude for three solid years, he didn't wear a stitch of clothing at all.
Saul prophesied nude before Samuel, and was called a prophet.
David danced nude before the Ark of the Lord, yes nude before God's ark.
Simon Peter worked naked while fishing
Jesus deciples were often nude while working simply because it was more comfortable.
The Greeks and Romans customarily excercised nude. The English word Gymnasium comes from the Greek word Gumnoss which means nude or naked.
In Jesus time it was not uncommon for people to work nude and share public baths (big ones, like swimming pools) while nude both co-ed and separate, this fact is historical.
Didn't Jesus die for our sins?
A major big question, and answers with Titanic implications.
Because people don't want to believe it is not wrong to be nude in the company of others.
Under certain circumstances is wrong to be nude.
Jesus says it is wrong to cause your brethren to sin, so if being nude causes him or her to gaze upon your nakedness and have sexual thoughts about you, then it would be wrong of you to be nude at that moment -it would also be wise of your brethren to turn away. If by wearing a certain type of garment would cause your brethren to have sexual thoughts about you then wearing that garment would be a sin too.
I meant Titanic.

So, who's sins did Jesus die for?

Everyone's sin, yes everyone's, starting with Adam and Eve. Jesus' death was the last sacrifice, the ultimate sacrifice to end all sacrifices, his blood washed away our sins, the sins of the world.
That means we no longer live under the law but under the grace of God, see Romans 6:14.
This means that as Christians, we are no longer bound by the law that the Jewish people were under before Jesus' death.
So why don't we believe that, or why don't our spirits believe that?
When God forgives us of our sin, our slate is wiped clean.

Jesus died for our sins. We are saints in the eyes of God. This means that our relationship with God has been put back on track, as it was when Adam and Eve were in the garden, before the bite.
We no longer live under the curse of the original sin.
John 3:16-17
16 For God so loved the world, that he gave his only begotten Son, that whosoever believeth in him should not perish, but have everlasting life.
17 For God sent not his Son into the world to condemn the world; but that the world through him might be saved.
II Corinthians 5:15:
And that he died for all, that they which live should not henceforth live unto themselves, but unto him which died for them, and rose again.

Clothes have become the symbol of success, remember the saying 'clothes maketh the man'. But is it? Does expensive clothing make the man rich, or just appear rich?
The clothing industry is the largest industry in the world because the sales departments got it right.
Fashion is simply a huge sales gimmick.
Clothing doesn't make the man any more than wall paint makes the house. It is his spirit, his soul that makes the man, what he looks like is irrelevant, at least in the grand scheme of things.
They say first impressions count the most but first impressions can be, and usually are, way off base.
Gen 3:21 Unto Adam also and to his wife did the Lord God make coats of skins, and clothed them.
So, after the bite, God gave his children clothing and we have been clinging to the idea ever since.
We became hard wired to the need for the fabric shield.
Every Christian believes he -I'm not going to write 'and she' here because you know I mean that- is forgiven so why is it so hard see that the forgiveness goes all the way back to the original sin when clothing first appeared. If it wasn't for the disobedience, clothing wouldn't be as popular as it is today.
I believe that we wear clothing, not to hide our nudity, but to hide from a sin that was committed thousands of years ago. A sin that has been washed away by the blood of Jesus.

Social, non sexual nudity, as in the naturist lifestyle is not a sin, it is ordained, because it is how God created us.

Yes there are times when clothing is necessary for protection against physical harm, but for the most part, clothing isn't necessary, such as the times spent in-doors, at the office desk, chilling at home, outside when the sun isn't too hot (be careful about sun burn), to name just a few.
And, of course, when one is in the company of those who find nudity offensive or uncomfortable.
While I write this I am nude, simply, because it is more comfortable.

“What's in it for me,” you ask.
It is a known fact that naturists have a strong positive body image because of their chosen life style.
They don't mind being nude in company nor do they mind seeing other people nude, not because of sexual reasons either but simply because they believe it is not the naked body that is sexual but the naked mind.
There are several reasons why social, non sexual nudity / the naturist life style / naturism is not wrong and could even be said to biblically correct.

Note; This is digest version. The original essay is 18000 odd characters long.
Mail me if you'd like a copy.