You know those time travel films where the world heads in two different directions because of a single incident. The sweetly named Butterfly effect which often has much darker consequences. 

Imagine that the human race had never become obsessed with covering up their bodies and that a lack of concern about being naked in front of others had remained. Clothes can still exist but they would have the purpose of protecting our bodies in certain circumstances and not for protecting our "modesty" or exposing our "sauciness."

What do you think the world would be like now? How would it be different? Maybe you think it wouldn't be different at all? 

It could be simple things like the use of beaches and parks, changing rooms, sports...It could be effects on society - would there be less abuse, less anger, less mistrust. How about our daily lives? When the weather is nice would we just wander the streets, work and drive naked? What clothes wouldn't exist? Would we have bothered inventing bras or swim wear? How about the global effects? Missionaries wouldn't have demanded indigenous people cover up.

How would a society that remained more body aware and body confident alter our current world? Remember this isn't about changing the attitude of the people of todays world on nudity, it is about the current attitude towards nudity never existing in the first place. I cannot wait to read your visions.

There may be cases where missionaries wrongly insisted that indigenous people cover up; but by and large I think that's a misconception. Suggested reading: "Someone Must Die" by Alan Foster.  His parents lived with the Yuqui people in the jungles of Bolivia for several decades, and never once suggested they cover up; and those people didn't even wear anything on their feet, much less anywhere else.

To respond to your scenerio... it is a very interesting concept. My speculation is that clothing would have come around for convenience sake at minimum.  We aren't as equipped as the animals, to live in adverse conditions unaffected. Also, people care about status and recognition and clothing is one simple way of achieving that.
  This may come across as stinkin' thinkin'... but nothing good goes very long before someone comes along and 'steps on a butterfly.' 

I'll have to agree with SamD50 and EdwardCharliontheBeach on this one.

My thought is not so much that clothing didn't come along but that we only use it to cover up the parts of us that we need to for the specific reason. Not that we live life naked but that we aren't afraid on certain parts of our body being seen or getting naked in front of others when nudity suits. A world where we throw a shawl over our shoulders to help with the warmth maybe but not worry about our genitals being exposed... where each part of the body is not a concern whether it is the elbow, ear, neck, breast, buttocks or penis.

When it comes to that, hasn't their been cultures pretty much like that? But yes, without further qualifications or objections, I agree. It'd be swell.

Here's a side tidbit that might interest you.  After the Fosters had been working with the Yuqui people for a couple of years, giving them gifts (machetes, buckets, bananas, first aid supplies, etc) to help them and build a relationship, the Yuquis began occasionally asking for articles of clothing. These were a people, apparently virtually oblivious to their own nudity and unashamed of their bodies; but for whatever unspoken reasons of their own, they began desiring to have shirts, and occasionally shorts, available to them. This was entirely without any encouragement from the missionaries. Food for thought.