Cool! Big kitty. I've only seen one once, very briefly along the side of the road before it disappeared into the brush (not counting zoos). It happened so fast my brain was trying to catch up and figure out what I was seeing. The long thick tail left no doubt, there's nothing else it could've been. I was driving in the wee hours of the morning. It was an area that is popular for no fee, disperse camping, so there were tents all around there, but I'm pretty sure I'm the only person who had any clue a cougar had just passed by.
Where are you at? Maybe Montana based on your user name?
I've seen bobcats several times, both while driving and hiking. Saw a lynx one time run across the road right in front of me just before I entered Glacier National Park. In several of the encounters the cat sat on it's haunches and watched me go by, didn't seem particularly concerned.
I go hiking all the time. I've never seen a cougar on trail, but I'm assuming that's only because I didn't look in the right place or they were concealed, not because I haven't been in close proximity to them.