Classified information, threats, bomb making instructions (borderline), categories of pornography, pirated media, libelous statements, trade secrets. Like I said, we may all agree that those things shouldn't be published--almost the entire world would--but some of them may be legal in some jurisdictions and not others, and there's a whole lot of grey area around the edges.
In general you can legally publish pretty much anything in the USA besides child porn or copyright infringement, everywhere else has stricter laws though.
There are numerous examples that have been given and I think all of them are disingenuous. Every single one of the examples harms people directly in some way. Burying a countries history intentionally is far different than censoring information that can harm people. Even under the 1st amendment we can actually get some of those examples. For example the media can publish classified but leaked material. The act of obtaining it without permission and releasing it to the public is illegal, but journalist are protected when reporting whistle blowing.
America is far from perfect, case in point the Red Scare, Japanese interment, civil rights atrocities. But that's not the issue. The issue is the tech companies specifically are forces that span the globe and those decisions and the ethical stances WILL and DO spill over into all societies they are apart of. Just look at oil companies, our desire for cheap oil and their desire for our money has driven wars, exploitation, corruption, etc.
It's easy for first world countries to ignore that because it happened else where, with tech companies though, those decisions leak into every country. Those policies are applied across the world. Apple's and other tech giants' stances on following the law regardless of morals and rights is applied everywhere. If that same law was here, they'd do it here.
That's the issue, not whether or not someone is putting medical information or classified information up for sale.
About 9% of Lebanon's parliament is the political party Hezbollah. They have a satellite TV station, Al-Manar. Americans hooking up satellite dishes to be able to watch it have been jailed, like Javed Iqbal.
As far as what the specific question is - what has Apple tried to publish that the US tried to publish, the answer is the same with regards to any of the PRC's giant domestic corporations vis a vis China. None of them tried to publish things blocked by their governments.
It's an odd thing to say amidst Assange's extradition, to bipartisan celebration. Of course they will get him for some technicality, as opposed to the attack on WikiLeaks - China is just less hypocritical about such things.
Trade secrets of other companies. HIPAA protected medical information. Classified information. Information related to the location of a person in the Witness Protection Program.