They're fairly common in the US, and used for almost any kind of official legal document. I've even had to have some forms on job applications notarized.
Almost anybody can be a licensed notary public, but you have to register with your local state agency. There are some basic eligibility requirements (which vary slightly by state, but usually involve state residency, legal age, clean criminal record, etc.), some filing fees, and some states require you to post a bond. You also have to buy your own embossing seal. The license has to be renewed every few years.
Aside from those state-designated requirements however, it's open to just about anybody, regardless of occupation. Typically legal secretaries are notaries, but also regular business secretaries may be notaries if their company needs such. Our receptionist at the Adult Education center I work for is a notary. Most copy shops or office supply shops will have a notary on staff. There's usually a small fee for having something notarized unless it's company business.
I thought about becoming one myself, until I realized one can't legally notarize one's own documents. I still want to buy an embossing seal someday, even if it doesn't declare me a notary because those things just look classy.
I once realized my driving license had been expired for four months (I somehow completely overlooked renewing it) when a notary asked to see it. She then refused to notarize my document because I didn't have a valid ID, which I found vexing, but she wasn't notarizing anything affirming my identity until I had a current valid photo ID.