That's a pretty delicate issue, and the answer depends on the personal view of the physicst you ask. I'm following the "minimal statistical interpretation", which just takes the minimal assumptions, i.e., the Born rule (together with the other mathematical postulates of QT, i.e., the projective Hilbert space for the (pure) states, self-adjoint operators to represent observables, unitary time evolution, etc.) to make the connection between the abstract formalism of QT with observations in the real world.
This implies that within the framework of quantum theory, after preparing an object in a definite state, which in the real world is given by an equivalence class of manipulations on this object to bring it into this state (e.g., preparing a beam of particles in an accelerator like the LHC), we only know probabilities about the outcome of measurements on the system. This implies that an observable has a determined value if and only if the system is in an eigenstate of the representing operator of this observable, and the corresponding eigenvalue is the value of this observable. Any other observables have no determined value, and the probability assignment according to Born's rule tells us with which frequency we can expect to find a possible value of this observable, when we repeat the experiment on an ensemble of many equally but independently from each other prepared systems.
There is no need for a collapse in this interpretation. The collapse hypothesis leads to a lot of inconsistencies within the framework of quantum theory, which cannot be justified by any observation today. First of all, the collapse hypothesis implies that quantum theory does not provide the complete description of the dynamics of the system, because with unitary time evolution there won't occur a collapse. This implies that there must be another theory describing the interaction of the measured system with the measurement apparatus. According to Bohr that theory is classical physics. However, there is no hint that on a fundamental level there is a "cut" between classical and quantum behavior. For macroscopic systems usually it is difficult to isolate them strictly enough from the environment to prevent decoherence. Through decoherence the behavior of the system becomes classical with high accuracy, but there is no principle reason to believe that quantum theory is invalid and classical theory must take over on a fundamental level. Nowadays one can prepare pretty large macroscopic systems in away that they show quantum behavior, including fascinating properties like entanglement, i.e., non-local correlations (not interactions!) between distant objects.
Another problem with the collapse hypothesis is related to entanglement, as was famously pointed out by Einstein, Podolsky, and Rosen: When the wave function of entangled far-distant objects would really collapse by measurement on one object, and this measurement implies the local interaction of the object with the measurement apparatus, has instantaneous causal implications for the other far-away object. This contradicts the causality structure of relativistic spacetime according to which no causal signal propagation can occur that is transmitted faster than the speed of light.
For all these reasons I think it is far more simple to abandon the unnecessary collapse hypothesis and stick to the minimal statistical interpretation!
