What's a good directory structure for larger C++ projects using Makefile?

Separating the .cpp of the .h file is not always a good solution. Generally I separate both of them when it is used as a library (public header in include and private header with the source code).

If it is a library, this structure is ok.

lib/ (class implementations *.cpp .h)
include/ (class definitions *.h) <- Only those to be installed in your system
tests/ (main.cpp for quick tests)
doc/ (doxygen or any kind of documentation)

If it is a application

src/ (source for the application)
lib/ (source for the application library *.cpp *.hpp)
include/ (interface for the library *.h)
tests/ (main.cpp for quick tests) <- use cppunit for this part
doc/ (doxygen or any kind of documentation)

Use the flag -I$(PROJECT_BASE)/include to specify the include path for the compilation

If it is a big project, it can be good to use tool like autoconf/automake or cmake to build everything. It will ease the development.

For those who find this question after 2020, an alternative modern and reasoned vision of "Canonical Project Structure" for C++ has been presented by Boris Kolpackov: http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2018/p1204r0.html

Briefly - no include/ and src/ split. All headers, sources, modules and unit tests go into one directory. Implementation details may be separated from public API by moving to <name>/<name>/details/ subdirectory.

<name>/
├── <name>/
│   ├── headers...
│   ├── sources...
│   ├── modules...
│   └── unit tests...
└── tests/
    ├── functional_test1/
    ├── functional_test2/
    ├── integration_test1/
    ├── integration_test2/
    └── ...

If you have many source files, it may also be a good idea to further subdivide your source directory. For instance, one subdirectory for the core functionality of your application, one for the GUI, etc.

src/core
src/database
src/effects
src/gui
...

Doing so also forces you to avoid unneeded relationships between your "modules", which is a prerequisite to nice and reusable code.