You'd have to decide where the frequency cut off will be. A young person with decent hearing can hear between 64-23,000 Hz or so. A dog can hear between 67-45,000 Hz, a cat 45-64,000, a bat 2000-110,000.
http://www.lsu.edu/deafness/HearingRange.html
But of course, pitch isn't the only thing that affects how well we hear something. Amplitude will have to be higher for sounds outside the middle of a species hearing range. This is a relief, or bat cries might sound like screaming to an animal who can hear that high.
You'd probably be able to hear high-pitched chittering of insects, birds, bats, and other small animals that fall outside our range of hearing how. I used to have a rodent hunting dog, and he'd stand by tall grass and cock his head like he was listening for the movements and squeaking of mice (much of it is beyond our range).
Also, there would be high pitched squeals and squeaks and friction sounds--clothes rubbing, shoes squeaking, fingers rubbing together. Things that sound high pitched to is now, like the squealing of tires or hinges, or other metal on metal sounds, would have an expanded range of sounds and probably sound louder to us too.
There's also a wealth of sounds that are below the normal range of human hearing. There are reports of various low-pitched hums or buzzes in various locales, for instance (Aukland, NZ is one) that a small number of people can hear but most can't. They don't always know what the source of these noises are, but sometimes they turn out to be sounds from local factories, or wind or wave resonance. I think the "Aukland hum" is still a mystery, but the people who can hear it have variable descriptions. Some say it's a bit like a diesel motor idling, others say it's more of an electronic hum or buzz.
You'd be able to hear thunder more keenly too at lower ranges. Interestingly, dogs aren't supposed to be able to hear ultra low sounds as well as we can (which sort of refutes the idea that they can hear earthquakes before we do), yet mine seem to be able to hear thunder before we do. Maybe it's not lower-pitched noises they're hearing there, but they're more sensitive to low amplitude sounds in that range than humans are.