Visa free travel usually, and special work visas like the deals between US and Canada or US and Australia. It's also used for retaliation in other ways, like when China revoked visa free travel for Norwegian citizens after Liu Xiaobo received the Nobel Peace prize, or Brazil photographing and fingerprinting only US citizens on arrival.
although the Australian visa deemed to match the US work visa for Australians is available without regard for nationality. I think reciprocity is common, but many states work in their own self interest first.
As an example from my personal experience, up until last year, Brazil required Americans to get a tourist visa. They also charged identical visa fees based on what Brazilians have to pay to visit the US as a tourist. On their website they made it plain that the whole motivation for the visa and fees was reciprocity. It stood out in my mind as funny because it seemed so petty.
I suspect one less petty motivation is to encourage the US to reduce visa restrictions for Brazilians. It wasn't actually reciprocal in practice because as far as I know the process of paying the fee as a USC visiting Brazil was far less involved than the process of applying for a US tourist visa (correct me if I'm wrong), not to mention an argument can be made that the fee on average has a lower impact on people from a higher-income country.
I think it is fairly onerous for both parties speaking as a US citizen who visited Brazil a number of years ago. Until recently you had to visit a Brazilian embassy and bring a postal money order as well as printed passport style photos and conduct a financial interview (to make sure you had enough money to leave).
Now it seems that you can do this all online, so ignoring the monetary component it was not any easier than a Brazilian person in my experience as a USC with many Brazilian friends.
For certain countries like Cuba and Iran, where relations are colder, there are "reciprocity tables" which give fees and restrictions for immigrants from there based on making comparable requirements to what their country requires of Americans.
Many countries are reciprocal to the US—ie, US citizens are made to face the same restrictions/difficulty entering country X as country X's citizens face entering the US.
What? Which part of our immigration system is reciprocal?