I think the definition in Wikipedia is simply bad because it depends on another debatable definition.
I prefer something which follows from an observation made by Ricard Dawkins in The Extended Phenotype (the following is my definition, but I think Dawkins had something similar in mind):
An organism is any system of components which depend on each other for survival and cooperate in proliferating potentially unboundedly.
A single-celled organism is by this definition an organism since it proliferates by coordination of its components.
A single-celled organism with organelles deriving from endosymbiosis (think mitochondria) is an organism: even though mitochondria do proliferate on their own inside the cell, they don’t do so outside of the cell, hence have a bounded proliferation only; and they depend on the cell as a host. On the other hand, they cooperate with the cell division.
Endosymbionts, on the other hand, are organisms because even though they depend on a host (and the host on them), they may theoretically switch host or even survive a limited time without a host.
Similarly, the cells in a multi-cellular organism can sometimes divide independently (in organs) but they cannot survive without the rest of the organism, and the unbounded reproduction of any organ in fact requires going via the germ line of said organism.
A virus which depends on a host to proliferate does not form an organism with the host since it doesn’t use the host’s germ line; if, on the other hand, it does use the host’s germ line (consider virally derived pseudo-genes on our DNA) then, yes, it forms a common organism with its host.
Is (mother + her unborn child) an organism?
I wouldn’t say so, since the child is only temporally part of the host.
Is an apple that's just fallen off a tree an organism?
Interesting; I’d say yes, as long as it retains the potential ability to proliferate (it’s a separate organism from the tree though).
Is (human + their microbiome) an organism?
No. Humans can survive (albeit only shortly) without a microbiome; in the same vein, the bacteria of the microbiome can change their host.
Unfortunately, this definition also has a drawback: there are organisms which cannot reproduce because they are sterile, yet they are clearly still organisms.
Note that other definitions (e.g. “an organism is a collection of components sharing common genetic material”) also don’t work universally since they also break down – the example of genetic commonality would preclude mosaicism and organelles derived from endosymbiosis.