I actually had a site bookmarked for this very reason that provided some good, sound advice. I've always heard that a cougar (mountain lion) generally doesn't let you see it unless its considering attacking.

>**100 yards away or more that is unattentive to you**

> - Avoid rapid movements, running, loud, excited talk.
> - Stay in groups; keep children with adults.

>Probability of risk is slight, provided your response is appropriate.


>**50 yards away with its ears up and attentive to you**

> - Hold small children; keep older children close to an adult.
> - Do not turn your back.
> - Look for sticks, rocks or other weapons and keep them at hand.
> - Watch the cat at all times.

>Probability of attack is slight for adults given proper response.
>Probability of attack is serious for unaccompanied children.


>**Less than 50 yards away, staring intensely at you, or hiding;**

> - All of the above steps, plus place older children behind adults.
> - Seek a safer location, or one above the lion, if available.
> - Do not run.
> - Appear larger. Raise arms, objects, or jackets above your head.
> - Prepare to defend yourself.

>Probability of attack is substantial.

>**Intensely staring, crouching and/or creeping toward you**

> - Take all the above actions.
> - Moving slowly, position trees, boulders or other large objects between yourself and the lion.
> - Do not lose sight of the lion.
> - Smile! Show your teeth. (A woman attacked at Cuyamaca Rancho State Park may have saved herself by baring her teeth, growling and staring the lion down as it approached her).
> - Make loud, menacing sounds, like yelling and growling.
> - Throw things if the lion is close enough to hit.
> - Use lethal weapons if you have them.
> - Pepper spray may be effective if lion is downwind and close enough.

>Probability of risk is serious if within 20 yards.

>**Poised to attack**

> - Prepare to defend yourself in close combat
> - Fight back.
> - Make menacing noises.
> - Keep eye contact with the cat.
> - Act aggressively toward the 
> - Use a stick to charge the lion, thrusting the stick toward its face.
> - No stick? Yell loud and run toward the lion with arms high.
> - Stay beyond striking distance of its paws.

Source: [Link][1]


  [1]: http://www.angelfire.com/co/KlueLass/lions/ljohnson.html