In the latest Beta the team allowed the Knife tool to work with Smart Guides: http://illustrator.uservoice.com/forums/333657/suggestions/36682372 — and it works.
But without Smart Guides (and definitely without Snap to Grid) the tool still works constrained to internal point grid.
Whoever decided A) 1 point is enough and B) it needs constraining — is a saboteur.

Knife should be just like Pencil, have the same Fidelity parameter in its Options (which now are just missing), and work in the screen space.

Cannot generate path based on mouse movement path.

There seems to be an issue with the path the Knife tool makes. The path keeps shaking and is not smooth.

The Knife is such a useful tool for cutting closed shapes, but I agree it needs more precision. It tends to smooth out as you draw, and it should allow us to pause to create a corner point—or at least have varying smoothness/fidelity settings like the Pencil tool. This is an old and overlooked tool, but highly useful. Users who are creating art with the Text to Vector feature would benefit from a tool that allows for precise cutting of closed paths.

I have the same issue and I need this tool to do shading- it's really irritating how it totally smoothes the drawn curve making it look compleatly diffrent to what i wanted to get.

I am holding out hope for a more powerful and accurate knife tool one day.. just don't cut small objects where I want at all.

I think the Knife tool default should be straight cuts rather than curved. If this were the case, you could draw a cutting path---point by point---very precisely. You can't do this now since you have to hold the mouse button down for each segment, release and then hold to begin the next straight cut. Keeping the mouse button down works fine for curved cuts. Make the curved cut operation the ALT-ernative.

Hi, I agree, I would be also very happy if this feature would be developed, as right now it is either useless, or very annoying. I have been using knife tool quite a lot for creating shadows on illustrations by dividing the basic colour into 1-2 shapes (instead of drawing and it drove me crazy and I actually managed to use the pen tool to cut out shapes the same way, but then I don't see the point of knife tool being there. There is so much potential in this tool and I would love to use it, drawing with it like a pen or brush but instead of drawing it would cut. Right now it cuts so randomly just doesn't make sense at all! :( Even though I can manage to reach the same cut with pen tool, but it is more complicated then "drawing" the shape I need and voila it's already a cut there! Like what knives are supposed to do.. Please please let this tool grow to something really useful!