India’s and China’s require more work than most countries for Americans, but the visas are full page stickers.
India’s includes a photo. I think the U.S. Visa does too, but I haven’t seen them for any other countries.
The Foreign Expert Certificate took the most work, but it’s definitely the coolest and takes the place of a visa in your passport. You can use it for any identity purpose in China like opening a bank account, train tickets, or police ID request. The only thing you can’t use it for is international flights.
The most noteworthy visas been issued are the ones given by territories that are not widely internationally recognized or openly disputed. A good example would be the Nagorno-Karabakh Republic, a de facto independent but unrecognized state established on the basis of the Nagorno-Karabakh autonomous province of Azerbaijan. While officially being part of Azerbaijan, access to Nagorno-Karabakh is only possible by ground transport from its guardian nation Armenia.
Another good example is Abkhazia, which is a partially recognized state controlled by a separatist government on the eastern coast of the Black Sea. Abkhazia considers itself an independent state. Georgia considers it a rogue occupied province of their nation. Abkhazia’s status is only recognized by Russia, Nicaragua, Venezuela, and Nauru.
In 2012 I slipped into Transnistria, a partially recognized state wedged between Moldova and Ukraine, from Odessa, without obtaining an entry permit. I bribed myself out of possibly uncomfortable circumstances when exiting the territory to Moldova. Unfortunately I didn’t get to keep any record of my stay there.