One non-Westphalian state is Monaco. But what are other non-Westphalian states in the world?
The Westphalian state system, while still used by many scholars, is, in a sense, anachronistic. In the post-War world, the UN Charter is the benchmark for 'state sovereignty'.
The first thing to note about the Westphalian system is that it was Euro-centric. It's primary purpose was to enforce the right of the King above that of the Pope. Consider this yourself, does this question even matter in today's world?
Then, the sovereignty outlined by the Westphalian agreement was conceived as absolute. In today's world, absolute sovereignty is impossible. The 21st century world operates under a complex interconnected system of International law and finance. State sovereignty is a compromise, a third link between the two.
But, if your question is strictly about Westphalian principles, that is state sovereignty, then, the simplest answer is that any state which is not sovereign is not a Westphalian state. At one end of the spectrum is any state under occupation, at the other, any which does not have absolute control over its domestic policies, which includes the majority of the states in the international system.
It's not a state per se since they don't fill the whole requirements made by the United Nations, but a good example of a non-Westphalian state is the Islamic State (ISIS). Why?
First, they don't recognize any treaty or peace conference made by the Western World; The Sharia Law is their command and no other peace agreement. A good look of this is when they took the Syria and Iraq's border freeing for transportation. In a documentary made by VICE the ISIS' press said the Sykes-Pykot agreement was made by the West without consultation of any Islamic party, therefore rendering it invalid for their "world".
Historically speaking we can argue that the Islamic World was considered by the Treaty of Westphalia "a sick world"[The Islamic World]. Since the Ottoman Empire banned all type of progress during the ages of the Treaty of Westphalia, they were treated just as observers.
A very important part of this idea is that the Islamic State is trying to do something, Westphalian-style but more medieval. Remember that before 1620 passed the Roman Empire, Holy Roman Empire, Caliphate and the Ottoman Empire. They're trying to reach a Caliphate but with the reach of something like the Ottoman Empire.
To see the basic things about the Westphalian "country", try: http://en.wikipedia.org/wiki/Westphalian_sovereignty