What about when some site is raving about a product, and pointing users to the product's website using an affiliate link. No disclosure at all. Is that also illegal? Because I think it would be great if it was.
Yes. That's a clear violation of the FTC guidelines. If you're presenting a review as an independent opinion without disclosing the fact you're making money from it, that's pretty much exactly what the FTC guidelines are designed to tackle.
If you're just providing links without specific endorsement it's probably fine.
Here's an easier read analysis of the FTC guidelines by the Washington Post:
Well, what's the difference between making an ad look like a legitimate endorsement, and endorsing a product even though you're financially benefiting because of the affiliate link?