Various creatures such as lycanthropes and golems are listed as being immune to damage from weapons not of a particular type. As unarmed strikes are not counted as weapons, but can be used as weapon attacks, do they ignore these immunities?
Unarmed strikes are negated by the immunities listed
According to the errata for the monster manual, the immunities in question have been changed from immunity to weapons to immunity to attacks. The exact quote is:
Throughout the book, instances of “nonmagical weapons” in Damage Resistances/Immunities entries have been replaced with “nonmagical attacks.”
Note that this had always been the case. Before any errata, unarmed strikes were listed as weapons, and the immunities referenced the weapons. Unarmed strikes were corrected to not be weapons, and the immunities were corrected to reference attacks instead of weapons.
No. Errata (as per xander's answer) aside, the intent of the rules is very clear in this regard. Unarmed strikes are not intended to ignore immunities.
E.g. for Lycanthropes
Damage Immunities: bludgeoning, piercing, and slashing damage from nonmagical weapons that aren't silvered.
Note that unarmed strikes are used like weapons (even though they're not really weapons) to deal bludgeoning damage. And since your fists, feet etc. are neither magical nor silvered, lycanthropes are generally immune to that damage.
A 6th level monk gains the ability Ki-empowered Strikes.
unarmed strikes count as magical for the purpose of overcoming immunity to nonmagical attacks and damage.
This benefit would obviously be meaningless if not for the fact that unarmed strikes are also generally affected by immunities.
Anyone trying to quibble about the letter-of-the-rule meaning unarmed strikes aren't affected is clearly on shaky ground.
On a related note, the important point about unarmed strikes not being weapons, is that: if you have an ability/spell to make a weapon magical, you cannot apply that benefit to your fists in order to bypass the immunities.