Does the use of ObservableList in JavaFX go against Model-View-Controller separation?
I disagree that using an ObservableList in your "model" class violates MVC separation. An ObservableList is purely data representation; it is part of the model and not part of the view. I (and others) use JavaFX properties and collections in model representations in all tiers of my applications. Among other things in there, I point out how I use JavaFX properties that are (or can be, at least) bound to JSF. (I should mention that not everyone agrees with the approach of using FX properties on the server side; however I don't really see any way to make the argument that they are somehow part of the view.)
Also, if you do
List<MachineMonitor> myNonObservableList = ... ;
ObservableList<MachineMonitor> myObservableList = FXCollections.observableList(myNonObservableList);
myObservableList.add(new MachineMonitor());
the observable list is backed by the non-observable list, so the change occurs in myNonObservableList too. So you can use this approach if you prefer.
Briefly, I don't think use of ObservableList breaks the MVC contract.
The rest, you may read or not as you wish, as it is quite annoyingly long.
Architectural Pattern Background
Observables are useful in MVC style architectures because they provide a way of feeding data back and forth between the MVC components through loose couplings where the model and view classes don't need to refer directly to each other, but can instead work with some shared data model which communicates data flow. It's not a coincidence that the Observable pattern and the MVC style architecture concept both originated around the same time at Xerox PARC - the things are linked.
As noted in Martin Fowler's GUI architectures, there are numerous different approaches to building GUIs. MVC is just one of these, kind of the granddaddy of them all. It is nice to understand MVC well (it is often misunderstood) and MVC concepts are applicable in many places. For your application you should use the system which feels best for you rather than rigidly following a given pattern (unless you are using a particular framework which enforces a given pattern) and also be open to adopting different patterns within an application rather than trying to shoehorn everything into a single conceptual framework.
Java Beans are a fundamental part of almost all Java programs. Though traditionally often only used in client apps, the observer pattern, through PropertyChangeListeners, has been, for good reason, a part of the Java Bean specification since it was created. The observable and binding elements of JavaFX are a rework of that earlier work, learning from it to build something that is both more convenient to work with and easier to understand. Perhaps, if the JavaFX observable and binding elements had existed ten or twelve years ago as part of the JDK, such concepts would be more generally used in a wider variety of libraries and frameworks than a couple of pure GUI frameworks.
Advice
I suggest considering the MVVM model and other GUI architectures.
If you want a dead-easy framework which follows a model, view, presenter style, definitely give afterburner.fx a spin.
I think the correct choice of architecture depends on your application, your experience and the size and complexity of the problems you are trying to solve. For instance, if you have a distributed system, then you could follow REST principles rather than (or in addition to) MVC. Whichever you choose, the architecture should aid you in solving the problem at hand (and possibly future problems) and not the converse. Over-architecting a solution is a common trap and is very easy to do, so try to avoid it.
Caveat
One caveat to consider is that observables necessarily work via side-effects which can be difficult to reason about and can be antithetical to the concept of isolation. JavaFX features some good tools, such as ReadOnlyObjectWrapper and ReadOnlyListWrapper, to help limit the impact (damage control if you like) on observables so they don't run amok in your system. Use such tools (and immutable objects) with reckless abandon.
Learn from Examples
For a simple JavaFX application which is built using observables, refer to tic-tac-toe.
For a good way to structure a large and complex JavaFX application with FXML based components, refer to the source code for SceneBuilder and SceneBuilderKit. The source code is available in the JavaFX mercurial source tree, just check it out and start learning.
Read up on the JavaFX UI controls architecture. Examine the JavaFX controls source code (e.g. Button and ButtonSkin or ListView and ListViewSkin) to see how concepts such as MVC can be applied using JavaFX structures. Based on that learning, try creating some of your own custom controls using the architecture that the JavaFX controls framework provides. Often, when you are building your own application you don't need to create your own controls (at least ones which derive form JavaFX Control). The JavaFX Controls architecture is specially crafted to support building libraries of reusable controls, so it is not necessarily generally suitable for all purposes; instead it provides a concrete demonstration of one proven way to get certain things done. Adopting and adapting proven solutions goes a long way to ensuring you don't reinvent stuff needlessly and allows you to build on a solid base and learn from the trials of others.
Regarding your Concrete Example
I advise you to go with:
The easiest way to link the "Model" and "View" of my program would simply be to change the "Model" class to have an ObservableList and not an ArrayList
Maybe use a ReadOnlyListWrapper to expose the ObservableList from the MachineMonitor to the outside world, so that nothing can modify it unduly.
Setup some other structure which encapsulates the view (for example a ControlPanel and ControlPanelSkin) and provide it a reference to the read only observable list of MachineMonitors. The ControlPanelSkin can encapsulate a TableView, a graph or whatever visual knobs and widgets you want to use for the user to monitor the machines.
Using such a structure effectively isolates your view from the model. The model really doesn't know anything about the UI at all and ControlPanelSkin implementation could be changed out to a completely different visual representation or technology without changing the core MachineMonitor system at all.
The above just outlines a general approach, you'll need to tweak it for your specific example.