Yes, biases which ideally you are aware of and try to account for.
For example, it would be stupid for me to entirely dismiss all of Wikipedia just because I know that there are some horribly biased articles and it'd be a disgrace if I shrugged such behavior off saying "hey, we all have biases, can't help it". That's what a child or even an animal would do.
They try to work hard and get rid of bias through various methods: peer reviews, precise methodology (randomization, blind tests etc.). And of course, even those sciences are not perfect, subject to biases, and evolve. This applies only to a subset of fields, in a lot of fields you either don't have the time to remove biases this way or it's impossible because it's inherently subjective. Besides, if you needed unbiased perfect opinions before taking any decision, the world would be stuck and slow.
I think we have a fundamental disagreement here. There is no bias in the statement "2 + 2 = 4". Nor is there bias in stating that "any two masses experience an attraction force proportional to the masses and inverse-square proportional to the distance separating them." Not less bias -- no bias.
There is a pretty strong bias in the statement "2 + 2 = 4" because math doesn't care about the encoding used to describe a sum. For example, in an alternative society the expression could be written with flipped number symbols, right to left or in a vertical layout. Axioms are also a form of bias.
Axioms would only be a form of bias if they were taken at random. It's not biased to take the axiom that repeatedly holds true in empiric testing, over others that do not.
1) The Monty Hall Problem (to be precise it hinges on ambiguity and the distinction between prior and posterior probabilities, but that is something most people aren't aware of and will get wrong the first time they see it, even people with knowledge of say Bayes' Theorem)
2) For several others, see Alon Amit's superb Quora answer to "What are the most interesting or popular probability puzzles in which the intuition is contrary to the solution?" ([2], login-walled). Mentions the very counterintuitive Penney's Game [0].
3) Berkson's Paradox, aka "People in hospital/getting treatment tend to have worse health indicators".
4) Asymmetric dice behavior is counterintuitive, when you first see it.
5) Benford's Law, on quantities occurring in nature (e.g. river lengths), as opposed to uniform distribution.
6) There are lots of counterintuitive things about Platonic solids.
7) Bayes' Theorem itself, superbly useful but possibly one of the things in probability most abused on a daily basis by bad journalism and bad statistics.
8) The Multiple Testing Problem/p-hacking/aka the xkcd "Green jelly beans cause acne"
and as a corollary:
8a) Most published (academic) findings aren't replicable, aka "Why Most Published Research Findings Are False", Joannidis (2005)
Great list! But I'm not sure the relevance? The intended point, which perhaps wasn't clear, was that logic / pure math as well as readily testable empirical theories are exceptions to the "everything is biased!" claim. There are in fact things that we can know with certainty, and that provides a foundation for a broader set of knowledge. The absolute relativist position is not just boring, but doesn't reflect reality either.
