The short answer is: don't use malloc for C++ without a really good reason for doing so. malloc has a number of deficiencies when used with C++, which new was defined to overcome.

Deficiencies fixed by new for C++ code

1. malloc is not typesafe in any meaningful way. In C++ you are required to cast the return from void*. This potentially introduces a lot of problems:

   #include <stdlib.h>
   
   struct foo {
     double d[5];
   }; 
   
   int main() {
     foo *f1 = malloc(1); // error, no cast
     foo *f2 = static_cast<foo*>(malloc(sizeof(foo)));
     foo *f3 = static_cast<foo*>(malloc(1)); // No error, bad
   }
   

2. It's worse than that though. If the type in question is POD (plain old data) then you can semi-sensibly use malloc to allocate memory for it, as f2 does in the first example.

   It's not so obvious though if a type is POD. The fact that it's possible for a given type to change from POD to non-POD with no resulting compiler error and potentially very hard to debug problems is a significant factor. For example if someone (possibly another programmer, during maintenance, much later on were to make a change that caused foo to no longer be POD then no obvious error would appear at compile time as you'd hope, e.g.:

   struct foo {
     double d[5];
     virtual ~foo() { }
   };
   

   would make the malloc of f2 also become bad, without any obvious diagnostics. The example here is trivial, but it's possible to accidentally introduce non-PODness much further away (e.g. in a base class, by adding a non-POD member). If you have C++11/boost you can use is_pod to check that this assumption is correct and produce an error if it's not:

   #include <type_traits>
   #include <stdlib.h>
   
   foo *safe_foo_malloc() {
     static_assert(std::is_pod<foo>::value, "foo must be POD");
     return static_cast<foo*>(malloc(sizeof(foo)));
   }
   

   Although boost is unable to determine if a type is POD without C++11 or some other compiler extensions.

3. malloc returns NULL if allocation fails. new will throw std::bad_alloc. The behaviour of later using a NULL pointer is undefined. An exception has clean semantics when it is thrown and it is thrown from the source of the error. Wrapping malloc with an appropriate test at every call seems tedious and error prone. (You only have to forget once to undo all that good work). An exception can be allowed to propagate to a level where a caller is able to sensibly process it, where as NULL is much harder to pass back meaningfully. We could extend our safe_foo_malloc function to throw an exception or exit the program or call some handler:

   #include <type_traits>
   #include <stdlib.h>
   
   void my_malloc_failed_handler();
   
   foo *safe_foo_malloc() {
     static_assert(std::is_pod<foo>::value, "foo must be POD");
     foo *mem = static_cast<foo*>(malloc(sizeof(foo)));
     if (!mem) {
        my_malloc_failed_handler();
        // or throw ...
     }
     return mem;
   }
   

4. Fundamentally malloc is a C feature and new is a C++ feature. As a result malloc does not play nicely with constructors, it only looks at allocating a chunk of bytes. We could extend our safe_foo_malloc further to use placement new:

   #include <stdlib.h>
   #include <new>
   
   void my_malloc_failed_handler();
   
   foo *safe_foo_malloc() {
     void *mem = malloc(sizeof(foo));
     if (!mem) {
        my_malloc_failed_handler();
        // or throw ...
     }
     return new (mem)foo();
   }
   

5. Our safe_foo_malloc function isn't very generic - ideally we'd want something that can handle any type, not just foo. We can achieve this with templates and variadic templates for non-default constructors:

   #include <functional>
   #include <new>
   #include <stdlib.h>
   
   void my_malloc_failed_handler();
   
   template <typename T>
   struct alloc {
     template <typename ...Args>
     static T *safe_malloc(Args&&... args) {
       void *mem = malloc(sizeof(T));
       if (!mem) {
          my_malloc_failed_handler();
          // or throw ...
       }
       return new (mem)T(std::forward(args)...);
     }
   };
   

   Now though in fixing all the issues we identified so far we've practically reinvented the default new operator. If you're going to use malloc and placement new then you might as well just use new to begin with!

new/delete + new[]/delete[]:

• new/delete is the C++ way to allocate memory and deallocate memory from the heap.
• new[] and delete[] is the C++ way to allocate arrays of contiguous memory.
• Should be used because it is more type safe than malloc
• Should be used because it calls the constructor/destructor
• Cannot be used in a realloc way, but can use placement new to re-use the same buffer of data
• Data cannot be allocated with new and freed with free, nor delete[]

malloc/free + family:

• malloc/free/family is the C way to allocate and free memory from the heap.
• calloc is the same as malloc but also initializes the memory
• Should be used if you may need to reallocate the memory
• Data cannot be allocated with malloc and freed with delete nor delete[]

Also see my related answer here