All things are lawful for me, but not all things are profitable.
1 Corinthians 6:12a
Essentially, the short answer is that, yes, Christians can watch rated R movies. Watching a movie with an R rating is not, necessarily, a sin. That said, there are a number of various nuances that we should probably take a look at with respect to this question.
The first, and perhaps most obvious question, is, "Why did the movie receive an R rating?" There are a number of different reasons why movies are rated as they are. Nudity, language, violence, etc. These are all factors that go into rating movies. Yet, even among these factors, there is a bit of nuance in them...at least as far as whether or not Christians can feel comfortable going to see them.
Let's take nudity, for example. I'm a big fan of the original Highlander movie. It's one of my favorites. Yes, I know, they didn't really leave the option open for a sequel and they made one anyway and it was terrible and awful and not very good, either. But, I digress.
In the first few minutes of the movie, there is a scene in a parking garage where a heated battle of swords ensues, but at one point during the battle, the camera goes to a parked car in which there is a couple who must have not had the means to get a room and the girl raises herself up to allow for a totally gratuitous view of herself topless. If this few seconds of film were not in the movie, it would have absolutely no impact on the plot or any other aspect of the story in any way, shape or form. It was completely gratuitous.
On the other hand, there is nudity in the movie Schindler's List as well. Those familiar with the movie understand that the nudity in that movie is not sexual in nature. There is no implication of sexuality and the scenes are included primarily for the purpose of showing how dehumanized the prisoners were in the German concentration camps.
Both films contained scenes with nude women. Yet, the point of the scenes differed dramatically. One could argue that Schindler's List could have, perhaps, found another way to make the point that they were making, but I think we can all agree that there is a distinct difference in the type and reason for nudity between these two movies. And we won't even get into those movies that are basically just about teenage sex romps where there really is no plot, but just a thinly veiled excuse to show nude women on the screen.
What about violence? Once again, one can argue that the violence in a movie like The Expendables is significantly different in nature from the violence in a movie such as Saving Private Ryan. Don't get me wrong, I've got Expendables 2 in my Netflix queue. I'm just trying to point out that these factors that go into rating movies have various levels of gratuitousness (is that a word?) which may help someone determine whether or not they feel a certain movie is or is not appropriate viewing.
The other factors that go into movie ratings are, it seems to me, similar to these in the sense that some movies display certain scenes for the sake of the scenes themselves and others include them because it makes a powerful point that is important to the plot or the understanding of the characters and environment in which the movie is taking place.
With all that said, and I'm going to be slamming myself just a bit here with this one, for all of you reading this who are thinking that it just comes down to a judgement call and for the most part R ratings are fine, let me make one last foray into scripture. Mind you, while I do think this is important (or I wouldn't include and and it wouldn't be in the Bible) you will still have to decide for yourself whether or not you're going to watch The Hangover Part 3 or something.
Finally, brethren, whatever is true, whatever is honorable, whatever is right, whatever is pure, whatever is lovely, whatever is of good repute, if there is any excellence and if anything worthy of praise, dwell on these things.
So, I guess the last question we have to ask ourselves about an R-rated film, or any film for that matter, is...."Is there some redeeming quality that can be realized from watching this?" Is there anything about a particular movie that is true, honorable, right, pure, lovely, of good repute, excellent or worthy of praise? Perhaps answering those questions can help you decide whether or not to watch a given movie.
If after all that, you decide you still want to watch movies that don't meet these criteria, I can tell you that you're not alone. Personally, as much as I know it doesn't meet any of the above criteria, I'm probably still going to watch The Expendables 2.