Why should I prefer to use member initialization lists?

Apart from the performance reasons mentioned above, if your class stores references to objects passed as constructor parameters or your class has const variables then you don't have any choice except using initializer lists.

For POD class members, it makes no difference, it's just a matter of style. For class members which are classes, then it avoids an unnecessary call to a default constructor. Consider:

class A
{
public:
    A() { x = 0; }
    A(int x_) { x = x_; }
    int x;
};

class B
{
public:
    B()
    {
        a.x = 3;
    }
private:
    A a;
};

In this case, the constructor for B will call the default constructor for A, and then initialize a.x to 3. A better way would be for B's constructor to directly call A's constructor in the initializer list:

B()
  : a(3)
{
}

This would only call A's A(int) constructor and not its default constructor. In this example, the difference is negligible, but imagine if you will that A's default constructor did more, such as allocating memory or opening files. You wouldn't want to do that unnecessarily.

Furthermore, if a class doesn't have a default constructor, or you have a const member variable, you must use an initializer list:

class A
{
public:
    A(int x_) { x = x_; }
    int x;
};

class B
{
public:
    B() : a(3), y(2)  // 'a' and 'y' MUST be initialized in an initializer list;
    {                 // it is an error not to do so
    }
private:
    A a;
    const int y;
};