Question

Why should would one replace the default operator new and delete with a custom new and delete operators?

This is in continuation of Overloading new and delete in the immensely illuminating C++ FAQ:
Operator overloading.

An followup entry to this FAQ is:
How should I write ISO C++ standard conformant custom new and delete operators?

Note: The answer is based on lessons from Scott Meyers’ More Effective C++.
Note: This is meant to be an entry to Stack Overflow’s C++ FAQ. If you want to critique the idea of providing an FAQ in this form, then the posting on meta that started all this would be the place to do that. Answers to that question are monitored in the C++ chatroom, where the FAQ idea started out in the first place, so your answer is very likely to get read by those who came up with the idea.

Answer 1

One may try to replace new and delete operators for a number of reasons, namely:

To Detect Usage Errors:

There are a number of ways in which incorrect usage of new and delete may lead to the dreaded beasts of Undefined Behavior & Memory leaks.
Respective examples of each are:
Using more than one delete on newed memory & not calling delete on memory allocated using new.
An overloaded operator new can keep a list of allocated addresses and the overloaded operator delete can remove addresses from the list, then it is easy to detect such usage errors.

Similarly, a variety of programming mistakes can lead to data overruns(writing beyond the end of an allocated block) and underruns(writing prior to the beginning of an allocated block).
An Overloaded operator new can over-allocate blocks and put known byte patterns (“signatures”) before and after the memory made available to clients. The overloaded operator deletes can check to see if the signatures are still intact.
Thus by checking if these signatures are not intact it is possible to determine that an overrun or under-run occurred sometime during the life of the allocated block, and operator delete can log that fact, along with the value of the offending pointer, thus helping in providing a good diagnostic information.

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To Improve Efficiency(speed & memory):

The new and delete operators work reasonably well for everybody, but optimally for nobody. This behavior arises from the fact that they are designed for general purpose use only. They have to accommodate allocation patterns ranging from the dynamic allocation of a few blocks that exist for the duration of the program to constant allocation and deallocation of a large number of short-lived objects. Eventually, the operator new and operator delete that ship with compilers take a middle-of-the-road strategy.

If you have a good understanding of your program’s dynamic memory usage patterns, you can often find that custom versions of operator new and operator delete outperform (faster in performance, or require less memory up to 50%)the default ones. Of course, unless you are sure of what you are doing it is not a good idea to do this(don’t even try this if you don’t understand the intricacies involved).

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To Collect Usage Statistics:

Before thinking of replacing new and delete for improving efficiency as mentioned in #2, You should gather information about how your application/program uses dynamic allocation. You may want to collect information about:
Distribution of allocation blocks,
Distribution of lifetimes,
Order of allocations(FIFO or LIFO or random),
Understanding usage patterns changes over a period of time,maximum amount of dynamic memory used etc.

Also, sometimes you may need to collect usage information such as:
Count the number of dynamically objects of a class,
Restrict the number of objects being created using dynamic allocation etc.

All, this information can be collected by replacing the custom new and delete and adding the diagnostic collection mechanism in the overloaded new and delete.

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To compensate for suboptimal memory alignment in new:

Many computer architectures require that data of particular types be placed in memory at particular kinds of addresses. For example, an architecture might require that pointers occur at addresses that are a multiple of four (i.e., be four-byte aligned) or that doubles must occur at addresses that are a multiple of eight (i.e., be eight-byte aligned). Failure to follow such constraints can lead to hardware exceptions at run-time. Other architectures are more forgiving, and may allow it to work though reducing the performance.The operator new that ship with some compilers don’t guarantee eight-byte alignment for dynamic
allocations of doubles. In such cases, replacing the default operator new with one that guarantees eight-byte alignment could yield big increases in program performance & can be a good reason to replace new and delete operators.

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To cluster related objects near one another:

If you know that particular data structures are generally used together and you’d like to minimize the frequency of page faults when working on the data, it can make sense to create a separate heap for the data structures so they are clustered together on as few pages as possible. custom Placement versions of new and delete can make it possible to achieve such clustering.

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To obtain unconventional behavior:

Sometimes you want operators new and delete to do something that the compiler-provided versions don’t offer.
For example: You might write a custom operator delete that overwrites deallocated memory with zeros in order to increase the security of application data.