I pretty much followed the standard procedures, but used ccmake to turned shared to off. Here's the gist of it:
sudo apt-get install updates
Install required dependencies:
sudo apt-get install build-essential git cmake cmake-curses-gui xorg-dev libgl1-mesa-dev libglu-dev -y
Install additional/optional dependencies:
sudo apt-get install libpng-dev libcurl4-openssl-dev libfreetype6-dev libjpeg-dev libvorbis-dev libopenal-dev libphysfs-dev libgtk2.0-dev libasound-dev libpulse-dev libflac-dev libdumb1-dev - y
Install documentation dependencies, too, if you plan on building docs:
apt-get install exuberant-ctags dvi2ps dvipdfmx latex2html pandoc
Clone Allegro 5:
git clone https://github.com/liballeg/allegro5 && cd allegro5
Make a build directory and navigate to it:
mkdir build && cd build
ccmake -DCMAKE_INSTALL_PREFIX=/usr ..
In the above, create and generate, then turned shared to "OFF" (just follow the prompts).
Make and install Allegro:
make && sudo make install && sudo ldconfig
Now everything should be good to go. When compiling, use something like this:
g++ -o example example.cpp $(pkg-config --libs --static allegro-static-5 allegro_image-static-5)
So don't forget the allegro*-static-5 and --static parts.
Doing all of the above resulted in an executable that worked on a fresh installation of Ubuntu 16.04. On that fresh install, I had to install libdumb1 and libopenal1 before running the game though. Maybe those could be statically packaged in as well, but I'm too lazy for that.