Does "natural" superposition of particles exist? While studying the basics of quantum computers, I came across Hadamard gates and learned, that these gates are used to put qubits into superposition meaning that these qubits are both, 0 and 1 at the same time. I've also learned that superposition is very susceptible to external influences and can be "destroyed" quickly.
Given that superposition seems to be so fragile: Does it exists naturally? Are there particles that are in superposition for a longer period of time?
 A: Yes, superposed states are ubiquitous. For example, the electrons in a molecule are not localized; this is a form of superposition. See Chemical Bonding as a Superposition Phenomenon for details, and also this blog post for a presentation of these ideas.
A: The canonical example is probably neutrino oscillations, where the flavor eigenstates are a superposition of the mass eigenstates, resulting in neutrinos changing flavors during the interaction-free evolution.  The experimental verification and consequences of this were recognized by 1995 Nobel Prize in Physics.
A: One of the common misconceptions that people starting out with QM often have is to think that a system is either in a superposition state or it is not. Actually superposition is only defined relative to a particular basis (such as the eigenstates of some observable).
If a system is in a state of superposition relative to one basis it is always possible to define a basis where it is not and vice versa. 
So for example a particle with a definite position is in a superposition of momentum states or a spin pointing up relative to the $z$ direction is in a superposition of up and down relative to the $x$ or $y$ directions. 
A: *

*I think you are asking about the quantum superposition of a particle's quantum mechanical property's states.

*of course people usually talk about the particle itself being in a superposition, but according to QM, we usually talk about that the particle's QM property is in a superposition, for example it's wave function

*you can talk about the particle's QM property's superposition, like that the particle spin's along the x axis is in a superposition of states

*yes you are right, the superposition exist naturally. On the other hand, when you talk about entanglement, that usually exist on purpose because we create entangled particles (it could happen naturally too, but not usually). But we do not create on purpose particles with superposition. Superposition is natural because it states that for all linear systems, the net response is the sum of each. That is naturally existing in every linear system. Therefore, particles' QM properties are in superposition until measured. So your question if they exist for a long time, yes a stable system that does not decay will exist in a superposition until measured. 
