Why do any serious philosophers at all believe that only one thing exists in the universe? What are the reasons they give? And are there any serious philosophers that believe no thing exists in the universe?
Monism does not necessarily posit that there is one thing that is the whole so much as everything is really one kind of thing.
Just to give one quick example to show it's less crazy than you think in modern thought.
Many of todays leading scientists and quite a large percent of philosophers are materialists. Materialists are a type of monist as they believe the only thing that exists is matter (you can try quibbling by pointing out energy, dark matter, etc., but these are ultimately differentiations on the same thing according to the theory).
Spinoza in his Ethics had proved Proposition XIV
"Besides God no substance can be granted or conceived"
which has a Corollary I with this:
“...only one substance can be granted in the universe...”
Surely, now we do not consider such proofs as proofs. However, it reveals some truth.
If one conceives two independent substances, she should accept that they would interact. An interaction would demand a common ground, therefore it will undermine the independence and a monism becomes inevitable.
One can point to Christian God - he can influence without being influenced, but one can argue that this construction is too abstarct or too artificial.
A contemporary philosopher who is defending a version of monism is Jonathan Schaffer, whose work can be found here.
The division of the world into separate "things" seems obvious, but may not withstand certain types (e.g. time-scales) of scrutiny.
Consider your body, for example: it sheds skin flakes; you eat and breathe; where does your body begin, and where does it end? Is it the same thing tomorrow, as yesterday? In what sense is it a thing that's objectively separate from other things?
The notion of "thing" is a mental construct, and the reason to differentiate one from another is entirely arbitrary. In a gaseous world, the notion of "thing" is very difficult to comprehend.
My own attitude toward monism is that of an agnostic, i.e. there is not enough evidence to suppose monism is false and it is unnecessary to believe it is true.
Whitehead & Russell's Principia Mathematica does not require the existence of more than one individual for its primitive propositions. The axiom of infinity is added in the middle of the second volume as a hypothesis for the existence of aleph-null.
The present scientific materialists is not the norm when you study the philosophical musings of many of the great scientific minds from Newton to Bohr to Planck to Einstein to Schrodinger to name a few - over the centuries. Their ideas of "God" were a monistic one.
A good reference is "Quantum Physics and Ultimate Reality: Mystical Writings of Great Physicists" By Michael Green; it is a collection of writings of various scientists, including Einstein, Bohr, Heisenberg, Schroedinger, Pauli, Eddington, Dyson, Bohm, etc. To quote one, Albert Einstein -
"..I am a deeply religious man. I cannot conceive of a God who rewards and punishes his creatures, or has a will of the type of which we are conscious in ourselves. An individual who should survive his physical death is also beyond my comprehension, nor do I wish it otherwise; such notions are for the fears or absurd egoism of feeble souls.
"Enough for me the mystery of the eternity of life, and the inkling of the marvelous structure of reality, together with the single-hearted endeavor to comprehend a portion, be it never so tiny, of the reason that manifests itself to nature....I maintain that cosmic religious feeling is the strongest and noblest incitement to scientific research...Those who acquaintance to scientific research is derived chiefly from its practical results easily develop a completely false notion of the mentality of the men who, surrounded by a skeptical world, have shown the way to those like-minded with themselves, scattered through the earth and the centuries...It is a cosmic religious feeling that gives man strength of this sort.
A contemporary has said, not unjustly, that is this materialistic age of ours the serious scientific workers are the only profoundly religious people....science without religion is lame, religion without science is blind....the main source of the present day conflicts between the spheres of religion and science lies in this concept of a personal God."
They all have a great affinity to a monistic concept.
A good reference to study the various monistic traditions, Eastern and Western, and their differences is David Loy's book "Nonduality: A Study in Comparative Philosophy"