Christians believe God created the universe from nothing. Do any believe he can reverse this process, effectively annihilating his creation, or some portion of his creation?
According to Catholics God chooses to sustain creation.
301 With creation, God does not abandon his creatures to themselves. He not only gives them being and existence, but also, and at every moment, upholds and sustains them in being, enables them to act and brings them to their final end. Recognizing this utter dependence with respect to the Creator is a source of wisdom and freedom, of joy and confidence:
Therefore it would seem that Catholicism believes that God can annihilate his creation, but it would be by choosing to stop sustaining it, rather than by actively destroying it. However, he chooses not to.
This is a good question.
First of all, there is a problem with you/us assuming that you are correct in saying that Christians, any Christian denomination, believes God created the universe, or anything at all, from nothing.
So, first I am going to address that. Then, the main question, which really can be answered separately but I'm not too sure how to prove that answer.
What God did do, according to the various Bibles (all of them) is "say" and that is what "made" "all that can be seen." God's Word. When God speaks, that is the material with which He creates. God's Word does not have to make sound as we know it. Merely communicating is also God's Word when God communicates, ie the burning bush that Moses saw, was communication, yet silent. Stuff like that.
Here, I am going to have to give you a lot of examples. Because this is important. God is not a man. He used "His Word" to create the universe and that is very important. God's Word is part of Him. In fact, it is both what He uses to speak with (communicate) and what is "the Way" to Him (for us). It flows both ways. It is "the river of Life" etc. Again, the Almighty is not bound by what is possible on Earth. His River of Life flows both ways, to and from Him.
John 4: 13 "Jesus answered and said unto her, Whosoever drinketh of this water shall thirst again: 14 But whosoever drinketh of the water that I shall give him shall never thirst; but the water that I shall give him shall be in him a well of water springing up into everlasting life."
Let's use the KJV because it's so universally accepted.
Genesis 1:3 "And God said, Let there be light: and there was light." KJV
See? God "said"
Now, that might seem (almost) nonexistent but let's go to some more examples.
Genesis 1:6 "And God SAID, Let there be a firmament in the midst of the waters, and let it divide the waters from the waters." (Emphasis mine.)
God said. In every case, God speaks something into existence, then maybe does something more to it. The universe itself, seems to not appear until "day" four.
More likely, this Earth was not in orbit around our Sun, with our moon around it, until day four. Not a real stretch of the imagination if you've watched the usual amount of Star Trek movies by now. Hubble has tracked planets, comets, moons, etc. that race across irregular paths and/or streaming past whole suns. Gallaxies merge and the planets all have to come into orbits or turn into moons all over again. It's business as usual for the universe we live in.
But in all your main Protestant and Messianic/Hebraic denominations they say God created the heavens and the earth by saying. That is, by using His Word.
It gets better than that. You have to remember that "God's Word" was not a reference to some written scrolls or books somewhere until thousands of years after men and women (and children) knew of God's Word as Him speaking. That a Bible now is known by that term is because, in it, what God spoke got written down and, of course, is revered by humans somewhere.
The Gospel of John, Chapter 1, verses 1-4 "In the beginning was the Word, and the Word was with God, and the Word was God. 2 The same was in the beginning with God. 3 All things were made by him; and without him was not any thing made that was made. 4 In him was life; and the life was the light of men. 5 And the light shineth in darkness; and the darkness comprehended it not...
Now, to the actual question. You have the Roman Catholic view on it. Which does change, by the way, depending on current Papacies. They do make a point of issuing statements (bulls) when clarifying past doctrines now made more sure or refuting old things.
Remember, not all "catholics" are the same denomination. A Greek Orthodox (denomination) might have a very different view on this or any doctrine. The Episcopal Church considers itself sometimes to be a "catholic" version of Christianity. Lutheranism is considered by others, sometimes itself, to be catholic.
Your mainline Protestants all believe God can do whatever He chooses to, destroy or create. It was long ago my experience with a particular group "the Friends" sometimes still called Quakers, that they believe in a god that is both Creator and Destroyer. Today, on attempting to document that, it fell flat. So then, one group I can't prove told me so several times, decades ago. And this proves true when I attempt to search old free Google books on the subject, etc. Not coming up with any real doctrinal statements on the subject.
The various views on what limits Him from destroying is His Goodness. It is that He is Good (they believe) and so His actions and His Mercy (mercy is a big one) limit how much retribution He will serve on anyone, or anything. Including our universe. Then, in all fairness, you'd have to ask them who worship a female God, who use She instead of He, or the neutral folks, that use an It pronoun for their Almighty god.
So then, the opinions, and yes, it comes down to opinions, issued or not, on the character of God, determine whether any one or any denomination believes God "can" destroy. All Christians believe He has the power to remove His creation from existence. What differs are what each one takes a stand on as to the character of (their) God that would limit Him from doing such a thing. A few offshoots which your average mainstream Christianity would deny as even Christian are open about their belief that their god both creates and destroys. Hitler's god, named Providence, was such a one. But i doubt even he believed in a god that would totally destroy all of creation. That's basic Satanic doctrine, not Christian, to be truthful about it.
Hitler's Theology: A Study in Political Religion By Rainer Bucher
Some, I don't doubt Westboro Baptist Church, believe in a god that would and could and probably will (if was real) destroy all that is created, someday. Finding proof of that belief is what's difficult. I just spent most of today trying to, using my usual resources, it wasn't found.
For example, not every soldier carrying a gun uses it. And of those who do, not all use it to destroy or maim/harm a human. Some might use it to stop an enemy truck or kill a deer for food. It very much depends on the character of the person carrying such "power." So, it would appear, each denomination's view of the God whom they serve. I use the lower case g for god in this respect because in studying out the varying characters of the varying god's, it becomes apparent that all are not one and the same god. If one has a god whose word did not, and/or could not, have made a whole universe simply by saying so, then that is not the God of which one can quote the Bible then saying did so.
I don't think many denominations have come out with official stands on this issue exactly because it has to do with whatever is latest popular views on what's "good" justice and what isn't. And excellent example of that is the way Sweden handles it's adjudicated prisoners and the way the USA handles them. Popular opinion greatly affects whole denominational stands. Both Sweden and the USA would consider how it's penal systems work and the values they hold to be "good" but the manifestations of those "good" ways of holding, maintaining, rehabilitation, are whole continents apart.
Another example is the former use of capital punishment all over in the Western nations, and now. What was considered right and just, is now more often considered rude, wrong, or even evil. I make no judgement on them myself here, just pointing out that's what I believe is keeping denominations from even wanting to make stands on such an issue as this one.
The Christian denominations (except for maybe the United Methodist and Roman Catholic, quoted in these answers) are not usually open about it.