C++ FAQ Celebrating Twenty-One Years of the C++ FAQ!!!
(Click here for a personal note from Marshall Cline.)
Section 13:
13.1 What's the deal with operator overloading?
13.2 What are the benefits of operator overloading?
13.3 What are some examples of operator overloading?
13.4 Is operator overloading supposed to make the class' code clearer?
13.5 What operators can/cannot be overloaded?
13.6 Overloading operator== to use string comparison?
13.7 Can I create operator** for to-the-power-of?
13.8 But which operators should I override?
13.9 Guidelines / "rules of thumb" for overloading operators?
13.10 Creating a subscript operator for a Matrix class?
13.11 Should my Matrix interface look like an array-of-array?
13.12 Part two of making my Matrix interface look like an array-of-array?
13.13 Designing classes from the outside-in vs. inside-out?
13.14 Overloading prefix/postfix forms of operators ++ and --?
13.15 Which is more efficient: i++ or ++i?
[13.5] What operators can/cannot be overloaded?

Most can be overloaded. The only C operators that can't be are . and ?: (and sizeof, which is technically an operator). C++ adds a few of its own operators, most of which can be overloaded except :: and .*.

Here's an example of the subscript operator (it returns a reference). First without operator overloading: 

class Array {
public:
  int& elem(unsigned i)        { if (i > 99) error(); return data[i]; }
private:
  int data[100];
};

int main()
{
  Array a;
  a.elem(10) = 42;
  a.elem(12) += a.elem(13);
  ...
}
Now the same logic is presented with operator overloading: 
class Array {
public:
  int& operator[] (unsigned i) { if (i > 99) error(); return data[i]; }
private:
  int data[100];
};

int main()
{
  Array a;
  a[10] = 42;
  a[12] += a[13];
  ...
}