Agile methodologies hinge on a model of collective code ownership - basically, the idea is:
I may work on module A this iteration and you on module B, but next iteration I may work on B and you on C.
No developer has sole responsibility for any piece of the system, we all own it together. If I need to update some piece of the system to implement my assigned user story, I can do it, with the caveat that unit tests should pass and probably some quality check should be met (e.g. peer review, etc.).
In any non-trivially sized team, this is probably a necessity; the alternative model, strict ownership of code, will just yield unnecessary gridlock, turf-wars, and code ghettos as developers operate unchecked in their own silo, hording knowledge, and protecting the sanctity of their individual assets at the expense of the overall architecture.
And even knowing this, that individual code ownership isn't really feasible in an organization, I still think that when we accept the model of collective ownership, something important is lost: craftsmanship.
Sure, Agile advocates would argue that pride of ownership just extends to the work of the team rather than just that of the individual. To some degree this does exist, but it's not the same. When we have ownership of something, whether a design document, an API, or a UI screen, it's our reputation on the line, our creativity and execution that make it a success or failure. We make decisions on our own, quickly, without having to reach team consensus, for good or for ill, accepting the consequences. And when it does succeed, we derive a strong satisfaction from knowing that someone found value in what we alone designed and created. We helped make something better, easier, faster. The freedom of owning our work is what makes programming fun...and meaningful.
Without ownership, this satisfaction is muffled. When people collectively own everything, no one owns anything in particular. Collective ownership often means collective design, and so there's less investment in the overall success, because, hey, these aren't necessarily my ideas, they're the group's. And because everyone's a stakeholder in all the code, decisions are often made via sophistry and compromise, producing an end design that often looks more like a piece of legislation and less like a piece of craftsmanship.
It reminds me of a favorite quote of mine from Steinbeck in East of Eden:
And now the forces marshaled around the concept of the group have declared a war of extermination on that preciousness, the mind of man. By disparagement, by starvation, by repressions, forced direction, and the stunning hammerblows of conditioning, the free, roving mind is being pursued, roped, blunted, drugged. It is a sad suicidal course our species seems to have taken.
And this what I believe: that the free, exploring mind of the individual human is the most valuable thing in the world. And this I would fight for: the freedom of the mind to take any direction it wishes, undirected. And this I must fight against: any idea, religion, or government which limits or destroys the individual. This is what I am and what I am about. I can understand why a system built on a pattern must try to destroy the free mind, for that is one thing which can by inspection destroy such a system. Surely I can understand this, and I hate it and I will fight against it to preserve the one thing that separates us from the uncreative beasts. If the glory can be killed, we are lost.
I know, to argue against collective ownership in the era of wikipedia, social media, and open source is probably insane. Working collaboratively obviously can produce high quality results, and benefit the collaborator as well.
Even still, talking to colleagues and friends that do software development on teams, I see this unsatisfied need to own. Just about every programmer has dreams about their own side project, where he makes the decisions, where he is responsible. It's this freedom which most of us need, and which produces works of craftsmanship.