If it is an application my first choice would be to ship a statically-linked single executable. I had the opportunity to work on a product that was shipped to 5 platforms (Win2K,WinXp, Linux, Solaris, Tru64-Unix), and believe me maintaining shared libraries or DLLs with large codebase is a hell of a task.
Suppose this is a non-trivial application which involves use of 3rd Party GUI, Threads etc. Using C++, there is no real one way of doing it on all platforms. This means you will have to maintain different codebases for different platforms anyway. Then there are some wierd behaviours (bugs) of 3rd Party libraries on different platforms. All this will create a burden if application is shipped using different library versions i.e. different versions are to be attached to different platforms. I have seen people shipping libraries to all platforms when the fix is only for a particular platform just to avoid the versioning confusion. But it is not that simple, customer often has a different angle to how he/she wants to upgrade/patch which is also to be considered.
Ofcourse if the binary you are building is huge, then one can consider DLLs/shared-libraries. Even if that is the case, what i would suggest is to build your application in the form of layers like:-
Application-->GUI-->Platform-->Base-->Fundamental
So here some libraries can have common-code for all platforms. Only specific libraries like 'Platform' can be updated for specific behaviours. This will make you life a lot easier.
IMHO a DLL/shared-library option is viable when you are building a product that acts as a complete solution rather than just an application. In such a case different subsystems use common logic simultaneously within your product framework whose logic can then be shared in memory using DLLs/shared-libraries.
HTH,