Auto-implemented getters and setters vs. public fields
Solution 1:
I tend to agree (that it seems needlessly verbose), although this has been an issue our team hasn't yet resolved and so our coding standards still insist on verbose properties for all classes.
Jeff Atwood dealt with this a few years ago. The most important point he retrospectively noted is that changing from a field to a property is a breaking change in your code; anything that consumes it must be recompiled to work with the new class interface, so if anything outside of your control is consuming your class you might have problems.
Solution 2:
It's also much simpler to change it to this later:
public int x { get; private set; }
Solution 3:
It encapsulates setting and accessing of those members. If some time from now a developer for the code needs to change logic when a member is accessed or set it can be done without changing the contract of the class.