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Can you use R to replace MATLAB?
Yes.
I used MATLAB for years but switched primarily to R in the last 3 years. At this point, they have much more in common than not. It partially depends on your field and use-case. And as Spencer Graves said previously, it also depends on which "church you happen to frequent". It's best if you look at the MATLAB toolkit vs. CRAN for a specific task before you decide.
A similar question asked on R-Help a few years ago and again more recently. David Hiebeler (at the University of Maine) maintains an extensive R/MATLAB comparison, and is the best reference on the subject. You can also review this comparison of basic functions.
Here are some of the things that I've observed in the past, none of which should be deal-breakers.
R is an environment for statistical data analysis and graphics. MATLAB's origins are in numerical computation. The basic language implementations have many features in common if you use them for for data manipulation (e.g., matrix/vector operations).
R has statistical functionality hard to find elsewhere (>2000 Packages on CRAN), and lots of statisticians use it. On the other hand, MATLAB has lots of (expensive) toolboxes for engineering applications like
I have used both R and MATLAB to solve problems and construct models related to Environmental Engineering and there is a lot of overlap between the two systems. In my opinion, the advantages of MATLAB lie in specialized domain-specific applications. Some examples are:
Functions such as streamline that aid in fluid dynamics investigations.
Toolboxes such as the image processing toolset. I have not found a R package that provides an equivalent implementation of tools like the watershed algorithm.
In my opinion MATLAB provides far better interactive graphics capabilities. However, I think R produces better static print-quality graphics, depending on the application. MATLAB's symbolic math toolbox is also better integrated and more capable than R equivalents such as Ryacas or rSymPy. The existence of the MATLAB compiler also allows systems based on MATLAB code to be deployed independently of the MATLAB environment-- although it's availability will depend on how much money you have to throw around.
Another thing I should note is that the MATLAB debugger is one of the best I have worked with.
The principle advantage I see with R is the openness of the system and the ease with which it can be extended. This has resulted in an incredible diversity of packages on CRAN. I know Mathworks also maintains a repository of user-contributed toolboxes and I can't make a fair comparison as I have not used it that much.
The openness of R also extends to linking in compiled code. A while back I had a model written in Fortran and I was trying to decide between using R or MATLAB as a front-end to help prepare input and process results. I spent an hour reading about the MEX interface to compiled code. When I found that I would have to write and maintain a separate Fortran routine that did some intricate pointer juggling in order to manage the interface, I shelved MATLAB.
The R interface cons
As a user of both MATLAB and R, I think they are very different applications. I myself have a background in computer science, etc. and I can't help thinking that R is by statisticians for statisticians whereas MATLAB is by programmers for programmers.
R makes it very easy to visualize and compute all sorts of statistical stuff but I wouldn't use it to implement anything signal processing related if it was up to me.
To sum up, if you want to do statistics, use R. If you want to program, use MATLAB or some programming language.