To reduce the level of misguided answers make s
Little benefit
On a good compiler for a modern platform, inline will affect only a very few functions. It is just a hint to the compiler, modern compilers are fairly good at making this decision themselves, and the the overhead of a function call has become rather small (often, the main benefit of inlining is not to reduce call overhead, but opening up further optimizations).
Compile time
However, since inline also changes semantics, you will have to #include everything into one huge compile unit. This usually increases compile time significantly, which is a killer on large projects.
Code Size
if you move away from current desktop platforms and its high performance compilers, things change a lot. In this case, the increased code size generated by a less clever compiler will be a problem - so much that it makes the code significantly slower. On embedded platforms, code size is usually the first restriction.
Still, some projects can and do profit from "inline everything". It gives you the same effect as link time optimization, at least if your compiler doesn't blindly follow the inline.