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The normal force obviously always has direction perpendicular to the surface of contact, but I'm a bit confused about its sense: is it going 'up' or 'down'? I've seen articles on the web that describe the normal force as going either way.

My own reasoning would tell me that since force of friction is dependent on pressure — which usually translates to the normal force —, the normal force should go 'down'.

Why is it sometimes shown as going 'up'? Or is that just the normal reactive force?

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It might be better to ask if the normal force is "toward" or "away" from the surface. Mark's answer still applies, but we take away the ambiguity related to orienting the problem. – dmckee♦ Sep 23 '11 at 14:47
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This word comes from math, eg : en.wikipedia.org/wiki/Surface_normal up or down has no influence, math doesnt know gravity. – Georg Sep 23 '11 at 15:36

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The normal force is a constraint force. It is whatever it needs to be to keep an object in contact with a surface.

Something like the top surface of the table I'm at now can only apply a normal force in the "up" direction. If I push down on the laptop, the table will exert a normal force up to cancel my push and keep the laptop in the same place. If I lift up on this laptop, the table will not exert a normal force down to cancel my lift; instead the laptop will accelerate up off the table. So for this table and laptop, the normal force is up. (Note, however, that this implies there is a normal force from the laptop on the table which points down.)

If I had something like a bead on a wire, the normal force would be the component of the force of the wire on the bead that points perpendicular to the tangent of the wire. That could be in any direction, depending on the geometry of the wire.

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Actually, I'd say the normal force is the one that keeps the object from going through the surface, not the one that keeps it in contact with the surface. – David Zaslavsky♦ Sep 23 '11 at 16:21
@David I see that as a loaded description, since it would pretty much imply that the normal force is always out of the surface. If there's a constraint force keeping something from being lifted up off my desk, that force would also be normal to the desk top and thus also a normal force. So it could do either - whichever is required by the constraint. – Mark Eichenlaub Sep 23 '11 at 16:37
But in order to have a normal force that keeps the object from being lifted off the desk, you would have to have something on the other side of the object pushing it against the desk. It would be a normal force not because it's normal to the desk, but because it's normal to the other thing. – David Zaslavsky♦ Sep 23 '11 at 18:54
@David I think this is just terminology. I could take imagine a deus ex machina force between the table and the object that holds the object down. In that case, the component of the force perpendicular to the desk would still be a normal force, as I'm using the term. If we imagine a magnet stuck on the ceiling of a bus, I'd describe the force holding the magnet to the ceiling as a normal force. "Normal force" is just describing the geometry, not any of the physical interactions. – Mark Eichenlaub Sep 23 '11 at 21:39
Interesting, I hadn't heard that usage of "normal force" before. Guess I'll have to remember that. (I wouldn't call the magnetic force a "normal force" in your example.) – David Zaslavsky♦ Sep 23 '11 at 21:46
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It depends. If you have an object in a table, this table exert a normal force in order to keep the object in rest. In this case the normal force goes up. The object also exert a force to the table going down and related to pressure. And surely this is the origin of your confusion.

Now think about an object that you are putting against the roof whit your hand. In this case the roof exert to the object a normal force going down.

The normal force goes toward or away the surface in order to dont let the object pass through the constrain.

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