How can I render the way the render preview renders? I'd like to be able to render in cycles without the annoying tile system, just letting Blender keep working on the overall image, until I like the way it looks. Just like when I hit shift+Z, with preview samples set to zero. Is there a way to do this?
Yes, you can easily do this.

In your render settings under Performance just check: Progressive Refine.

Use very high samples and just stop the render, when you are satisfied with the way it looks.