Where does 'you' end, and 'not you' begin? That's really the philosophical question at the core of this.
Your heart is so undeniably at your core that it's used as a synecdoche for you. From there we proceed outward, or superficially, in medical terms. Your muscles, subcutaneous fat, blood vessels, and dermis, all decidedly 'yours'. Your half-dead half-alive epidermis? No, still yours. Some people would not even have a problem considering the dead skin cells and hair you shed around your house part of you. But what about the water vapor and radiant heat the pores in your skin are constantly giving off, that you can't see? When you get up at a restaurant and leave your seat warm, can you say that you've left a part of yourself there?
Then there are things like clothes and accessories. In a way they're definitely a part of you. It says something about you to all observers when you like something enough to attach it to your body. Certainly how you're able to make your way in the world, from giving the right impression at that job interview to getting sure you don't get stung harvesting that honey, depend on you adorning yourself, enhancing your body, the right way. I see little problem with any concept of ownership applying to clothes and accessories. There are few advantages, and some problems, to be had by treating most such items as common property to be passed around and used by everyone.
The food (and drugs) you eat becomes you. You certainly own it once it's past your lips. But the problem is, food doesn't generally go straight from its natural source into your mouth very often -- we just don't have enough land on earth for us all to forage for all our meals. So we farm. But for farming to work at feeding society, we need social contracts whereby every unit of foodstuff, from its harvesting to its consumption, is at all times earmarked as 'about to be consumed' by a particular person or group of people. We treat it as just as much a violation of someone to take a tomato out of their field as to reach in their mouth and forcibly pull it out, and we do that by extending the food's status of 'about to be consumed' backwards in time from being on the fork. Compare it in physics to the electrical potential between two charged plates -- it's a potential consumption, and we call this the right to consume. This is the essence of the concept of ownership.
I think the concept of ownership only gets controversial when you're talking about things that don't indisputably become a part or extension of your body. It seems easy, at first, to argue that you're the owner of all you create yourself. But that gets problematic quickly, because, as you can see with the example above about your body warmth on a restaurant seat, we're constantly making marks, deliberate and not so deliberate, on many things in our worlds, so it cannot be said that physically altering something confers ownership to you. What I have seen argued passionately, however, is that expending great personal effort at molding or maintaining something, without ever having such efforts stopped or questioned by anyone, merits its ownership by the effort expender. At which point in the process, though? If I carved a boulder that nobody cared about, on a piece of land nobody cared about, into a sculpture, and somebody hired a surveyor and determined it was on his land after reading about it in the news, would I have the right to cart it away? What if the alleged landowner stopped me halfway through the carving?
I find it interesting that the definition of the word 'consumption' has been extended to include the acquiring of things that do not become a part of your body, and only sporadically serve as an extension to it, in the same 'exclusive potential to use' fashion as food that I outlined above. Now there are two 'as if's in the mix: if an item is marked in our minds as 'consumed', to touch it is as much a violation against its consumer as if we were reaching inside his mouth and touching it if it were a food.
The purpose of society granting a person exclusive rights to the use and ultimate fate of a thing (including the rights to permanently transfer these exclusive rights!) is to provide a carrot of positive motivation for people to toil on behalf of society. Conversely, when people toil in ways that society deems not in society's best interest, society strips them of the exclusive rights to things -- think fines and seized property.
I for one do not share the libertarian's dream of everything being privately owned. There are certain resources that are just better managed for everyone's good when no one person or private group is granted ultimate say in their fate. Coral reefs are one example. Roads are another. It's as silly and extremist as the Communist dream of everything being common / nothing being owned -- a situation in which payoffs for work are less tangible, and thus it's harder to motivate workers and convince them their efforts are worth it.
I very much like the way ownership is handled in intentional communities and tight knit groups. Everyone chips in a certain amount from their salary to a common pot, and this goes to purchasing items for the community that everyone can use. I always thought it was silly to buy my own circular saw when I didn't use one more than a couple of times a year. I'd much rather live in a community arrangement that owned a common circular saw that I could use, providing no one else needed it that day and I always returned it in good condition. I'm more than happy to loan tools and other durable items like this to people I know will take care of them and return them. It's just excessive to own my own everything, I say.
Still, there are some things I'd want my own of, like clothing and hygiene products. It's just that I'm willing to draw a smaller radius of 'mine and only mine' than some people.