According to quantum theory, which is the most comprehensive theory ever, which just means that there's not a single observation which contradicts it, and it was tested very carefully even in its most astonishing aspects, which all have to do with "entanglement", describing on the one hand "randomness" on a fundamental level (i.e., observables on parts of an entangled quantum system do not take determined values) but on the other hand also "stronger correlations than classically possible" when these observables are measured (the violation of the so-called Bell inequalities and related predictions of socalled "local realistic hidden-variable theories", which are realized by the classical, i.e., non-quantum, description of Nature).
The double-slit experiment is an example for the fact that certain aspects of the behavior of particles (but also macroscopic bodies) cannot be described in any way within classical physics. According to what was discovered in connection with quantum theory in 1926, e.g., an electron is neither correctly described as a classical point particle and the laws of (Newtonian or relativistic) mechanics nor as a classical field, but one needs in a sense both descriptions. In the old quantum theory (discovered by Planck, Einstein, Bohr, and others in 1900-1925) this was dubbed "wave-particle dualism", but it was always clear that this is not a consistent picture but just a set of more or less empirical rules. With modern quantum theory, discovered in 1925 by Heisenberg and then worked out in terms of three different mathematical descriptions by Born, Jordan, and Heisenberg ("matrix mechanics"), Schrödinger ("wave mechanics"), and Dirac ("transformation theory"), the inconsistencies have been resolved by Born's probability interpretation of what's called a "quantum state".
According to quantum theory it depends on how the particles are prepared initially (defining its quantum state before measurement) and what is measured in a given situation. This has nothing to do with consciousness of the observer, and no esoterical mechanism of realizing measurement results by a conscious being is needed, but just the knowledge about the interactions of the measured system with the measurement apparati, and this is part of the general physical laws as described by quantum theory.