What items are forbidden to take when traveling to the US that would be OK in most other countries?

The full list of items restricted from being brought into the United States, is maintained by the US Customs and Border Protection agency, and can be found here.

Aside from the usual agricultural and weapons restrictions, be aware of the complete ban on the importation of Cuban made items, and the peculiar regulations regarding Absinthe.

Also, be advised that several US States have their own specific and unique restrictions on imports - particularly of alcohol, fruits, vegetables and other food items - that may be more stringent than federal laws. For example, the State of Hawaii imposes significant restrictions on the free movement of plants, fruits and vegetables.

Finally, as Mark Mayo notes, there is also a comprehensive list of items not allowed on an Airplane traveling within or into the United States, though for the most part, these are common sense and/or widely known and advertised.

Haggis is prohibited. Traditionally haggis is made with sheep lungs, which have been banned from food in the USA since 1971.

There have recently been calls to end this ban, see a report from The Guardian - Scotland to petition US to bring back haggis. Though I don't think the law has changed yet.

Even though sheep lungs are a traditional ingredient, not all haggis recipes use them. So some types may be allowed in the USA. There is vegetarian haggis available, which often tastes just as good, and would probably avoid any import restrictions.

Some quick Googling for other's experience (as I have been fortunate enough to never have anything but a screwdriver confiscated while travelling in/out of the USA) turns up mostly things that are either agriculture related (any sort of dead animal or a dead animal product) or controlled substances (even "ordinary" things that are not prescription but may be of uncertain origin) and most importantly, counterfeit items. The US is keen (probably more so than just about every other country) to vigorously enforce copyright rules and things like bootleg DVDs or even children's toys that are of unlicensed origin can be subject to seizure. Luxury items like fake rolex watches will be scrutinized too.

Here is a basic list of stuff to leave at home that might be OK in some/all other countries:
1: Anything that just recently died
2: Anything that might grow
3: Anything that might be counterfeit
4: Any food that you aren't going to eat before you get to the US CBP checkpoint (you either don't need it because its available in the USA, or if it's not then it's probably banned for some reason or another so leave it at home either way).

Also as others have explained, in case you are new to traveling abroad you will be subject to at least two (more if you are going through other countries) searches. One will be before boarding your US-bound flight, where you and your carry on belongings are subject to the TSA regulations to protect flight safety (things like potential explosives or weapons) and another when you arrive in the USA and want to disembark the airport (to officially enter the USA), which is the US Customs and Border Protection check that screens all your belongings for "odd" things like dead animals, counterfeit goods, large sums of cash, etc.

Since rules change over time from country to country, and we're unlikely to go through every item comparing it to every country, the best solution is to go to the source - the TSA.

Their list of Prohibited Items is updated regularly and is extensive and thorough. There are some perhaps unexpected items, but often with good reason - certain chemicals, for example, and you don't want a vehicle airbag going off in the hold, I guess. It's good to see that snow-globes are usually permitted(!).