The number one rule about edge tool safety is:
Always keep both hands behind the cutting edge of your tool.
This rule is absolute, and if you follow it absolutely, you'll absolutely never cut yourself.
My friend Dean is using the paring technique described in Moxon. Notice where his hands are in relation to the blade.
When working with chisels I use one of two basic grips: The Moxon grip (above)
and the carvers' grip (below). In both cases, both hands are behind the edge.
These grips need to become your "home" position. This takes practice.
But I think the reason guys break rule number one is because their work
holding isn't holding. So let's consider that.

Philadelphia Museum of Art conservator Christopher Storb uses a carving grip to shape a cabriole leg.
Get smart about workholding:
If your workpiece is slipping in the vice such that you need a hand to
support it, you're doing something wrong. Don't rely on friction
(clamping effect of clamps or vises) to react your effort. Use the vise
or clamps only to position the work and react your effort with a wall
(your bench IS against the wall isn't it?) a planing stop, bench hook or
the like. Take a minute to secure your workpiece. The time you waste
will be offset by the time you'll lose if you cut yourself.
This rubber mat, a piece of a carpet pad from IKEA, really helps secure work. I recommend using it. Likewise, super-hard, polished workbench tops are probably a mistake. This pad works so well, I can smooth this board without a planing stop. I'm not suggesting you give up your planing stop. But this is a nice way to increase friction and keep your work from slipping. Use it in addition to your planing stop, vise, and holdfasts.
The right tool for the job:
You really shouldn't need excessive force for most woodworking
operations. If you find your work needs more support than your bench can
provide, maybe you need to consider using a different tool. Dull tools
can also be the cause of needing excessive force. When you take that
hand off the back of the chisel, stop and think; "Is this really the
best way to do this?" Even when it's the fastest, will the time you save
with your hatchet offset the time you wait in the local emergency room?
When to make the trip?
I think many of us have been programmed to think of stitches as only
appropriate for serious injurues. Why make a Federal case out of a
small cut? Don't think of stitches or the number of stitches as
indicative of the seriousness of an injury. You go for stitches when
you need to go for stitches. Here are my untrained thoughts on the
subject:
When you have excessive bleeding, bleeding that doesn't stop within a
few minutes, go to the emergency room. Don't mind how deep the cut is.
If you can't stop the bleeding quickly, go.
Any deep cut in a joint area really will benefit from stitches, even
when the cut isn't bleeding perfusely. You want to be able to
close a wound and immobilize it. That's what stitches do. They speed
healing and stave off infection. Chances are, if you cut yourself at
10pm on a Saturday night in my neighborhood, you may be waiting 8 hours
to be stitched. You can pack it in for the night, apply a gauze pad and
tape as best you can, and head to the hospital in the morning. I think
you can go many hours between the time when the injury occurs and when
it is stitched.
Don't be afraid of your edge tools. Just make sure you are using a
technique that won't allow you to cut yourself and be prepared it you do.
Adam