Cougars definitely sound eerie. I've never heard one in person, thankfully, and I hope I never do. I live in California, and cougars are, supposedly, all over the state. Still glad I've never heard or seen one, though.
One of the eeriest sounds I've ever heard (well, does hearing them online count?) came from a video someone posted on YouTube. They claimed that it was a sasquatch, and although I think it's highly unlikely that they exist (just my opinion...), the sound is still pretty scary regardless. The people who caught the audio filmed about 15 minutes of it, I think.
On occasion, you can hear what sounds like dogs in the background. But I have no idea what the continuous roaring could be. o__o
VIDEO https://www.youtube.com/watch?v=wTsdbKUwenI Aside from that, there was one time several years ago in April that I woke up at 4:00 AM to a long, snarling sound that came from the ravine near my house. It sounded like a huge cat, and my first thought was "cougar." Oh my gosh, it was scary...I lied in bed with my eyes wide open, still as a statue, trying to figure out what on earth was making that noise. Another one soon followed after that sounded like a wounded cow, and I thought maybe a cougar had killed one on the ranch in the valley. The howling and moaning went on for a long time, and it actually wasn't until years later that I found out the noise had come from mating bobcats.
Super creepy!