Besides the technical implications of static vs dynamic libraries (static files bundle everything in one big binary vs dynamic libraries that allow code sharing among several different executables), there are the legal implications.
For example, if you are using LGPL licensed code and you link statically against a LGPL library (and thus create one big binary), your code automatically becomes Open Sourced (free as in freedom) LGPL code. If you link against a shared objects, then you only need to LGPL the improvements / bug fixes that you make to the LGPL library itself.
This becomes a far more important issue if you are deciding how to compile you mobile applications for example (in Android you have a choice of static vs dynamic, in iOS you do not - it is always static).