I'm not a developer.
I'm not a coder.
I'm not a WP guru.
I am a little guy that has about 100 client websites out there and they all work to the satisfaction of each and everyone of my clients. When I started building websites, I was even more ignorant than I am now, so about 20 of my websites have had changes made to the core files, because I didn't know any better. Do I remember what those changes are or where I made them, not so much.

I see people above trying to differentiate between minor and major releases. That's nice in theory, but the real life fact is that I have pressed update in instances of either type of update and had things break. I understand when I read that "minor" updates don't affect API's and such, but honestly, I have had sites break from pressing update on both types of updates.

Just standing there and telling me that I shouldn't have a choice in the fashion in which my site components, whether WP core, theme and plugins, update is a none starter. Someone above said that "the only thing we have to fear is ourselves" is a nice soundbite, but not really rooted in reality.

The choice must be very clear and upfront for each person to decide for each of their websites. I'm not sure how someone can make such a blanket statement such as "If a plugin is compatible with 3.7, it’s going to be compatible with 3.7.1, 3.7.2, 3.7.3, etc.", when this is just not true. Just Google "the only thing I did was apply a "minor" upgrade and now my xyz doesn't work any more." We can't all be making it up.

On an unrelated note Jeffro, the reality above is the one that I live AND I get to take a months vacation every 8 months or so. :-)