R is one of those programs that I prefer to install from source code on Linux. This is mainly because, as a package developer, I frequently install nightly R development builds anyway for package testing, and for general computing I like to work with the most recent stable release (which is updated semiannually).

R's use of system BLAS (basic linear algebra subroutines) and LAPACK libraries is of particular importance to me because I often work on problems with significant linear algebra components. I prefer to build R with the default (and slow) shared reference libraries and then post-installation swap out libraries using symbolic links as described in the R administration manual here: https://cran.r-project.org/doc/manuals/R-admin.html#Shared-BLAS This approach adds an extra post-installation step, but makes it easy to experiment with lots of different BLAS libraries by simply changing a link.

If you're on Windows systems, this old talk http://goo.gl/gcPezs has a short section on installing R with a high-performance BLAS library on Windows. (It's a bit old now and might need to be updated, but the general idea is there.)

Here is how I build and install R on Debian (Ubuntu)-like Linux systems, shown using the latest stable version of R at the time of this writing.
Prepare your operating system to build R, installing required dependencies
sudo apt-get build-dep r-base

# Depending on your OS you might also want (pick your favorite CURL variant)
sudo apt-get install libcurl4-gnutls-dev

# Download R source code
wget https://cran.r-project.org/src/base/R-3/R-3.3.1.tar.gz

# Uncompress R source code
tar xf R-3.3.1.tar.gz

# Configure R
# --enable-memory-profiling (compile support for Rprofmem--useful!)
# --enable-R-shlib  (needed by RStudio if you're in to that kind of thing)
# Note that --with-blas and --with-lapack are set by default to use
# the reference versions, as is the  --enable-BLAS-shlib setting (except on AIX).
# R will be installed into /usr/local by default, OK with me!

cd R-3.3.1
./configure --enable-memory-profiling --enable-R-shlib
make -j 4     # change the '4' to the number of CPUs you've got for faster compilation
sudo make install
At this point, R is installed with reference BLAS and LAPACK libraries. These are great for testing, but don't use threading and even more importantly don't use vector floating-point CPU instructions. That means that things like matrix multiplication, eigenvalues, and SVDs will run more slowly than they could on nearly all processors. The Open BLAS project is an open-source version of the superb Goto BLAS library. It provides extremely good use of vectorized CPU instructions and CPU caches and support for OpenMP threading, and its performance rivals and sometimes exceeds the best commercial BLAS libraries like the Intel MKL (depending on your processor of course). Here is how I enable OpenBLAS for R on my Ubuntu system:
sudo apt-get install libopenblas-dev
cd /usr/local/lib/R/lib
sudo mv libRblas.so libRblas.so-reference      # keep a copy for posterity
sudo mv libRlapack.so libRlapack.so-reference
sudo ln -s /usr/lib/openblas-base/libblas.so.3 libRblas.so
Optionally, also link the R LAPACK library. This step is generall much less important for overall performance, and depending on the libraries used might not even work (LAPACK is less well-covered than the BLAS API in some libraries, so some important functions might be missing).
sudo ln -s /usr/lib/openblas-base/libblas.so.3 libRlapack.so
Your machine is now equipped with R + a great BLAS/LAPACK library!

SMT/Hyperthreading

If you're using the Intel MKL BLAS library, then you don't have to worry about this section. If you're using OpenBLAS or some other OpenMP-based threading BLAS library (including the AMD ACML BLAS), then this section can improve your performance! The MKL BLAS knows how to deal with SMT optimally on its own. Some Intel systems (and soon, some new AMD Zen processor systems) can run more than one thread per physical CPU core, sometimes called hyperthreading or simultaneous multi-threading. This can work really well for mixed integer/floating-point workloads, but can sometimes slow things down for heavy floating-point only computations (because there is only one floating point unit per core typically). If hyperthreading is enabled on your system, you'll want to start R so that it is limited to using the total number of physical threads on your system in OpenMP code by setting the OMP_NUM_THREADS system variable. For instance:
OMP_NUM_THREADS=4 R
tells R to use at most 4 threads, corresponding to a computer with four physical CPU cores. If you don't specify a thread limit, OpenMP defaults to using the maximum number of threads reported by the system, which may be too many for floating point operations. Note! Some processors have one floating point unit per core, others might not. For instance, the AMD Opteron 6380 processor has only one floating point unit for every two CPU cores. You can set this as default by putting a line like:
echo "export OMP_NUM_THREADS=4" >> ~/.bashrc
in your bash start up file (assuming you use the bash shell, which you should!).