Can I use if (pointer) instead of if (pointer != NULL)?

You can; the null pointer is implicitly converted into boolean false while non-null pointers are converted into true. From the C++11 standard, section on Boolean Conversions:

A prvalue of arithmetic, unscoped enumeration, pointer, or pointer to member type can be converted to a prvalue of type bool. A zero value, null pointer value, or null member pointer value is converted to false; any other value is converted to true . A prvalue of type std::nullptr_t can be converted to a prvalue of type bool ; the resulting value is false .

Yes, you could.

A null pointer is converted to false implicitly
a non-null pointer is converted to true.

This is part of the C++ standard conversion, which falls in Boolean conversion clause:

§ 4.12 Boolean conversions

A prvalue of arithmetic, unscoped enumeration, pointer, or pointer to member type can be converted to a prvalue of type bool. A zero value, null pointer value, or null member pointer value is converted to false; any other value is converted to true. A prvalue of type std::nullptr_t can be converted to a prvalue of type bool; the resulting value is false.

Yes, you can. In fact, I prefer to use if(pointer) because it's simpler to read and write once you get used to it.

Also note that C++11 introduced nullptr which is preferred over NULL.

Question is answered, but I would like to add my points.

I will always prefer if(pointer) instead of if(pointer != NULL) and if(!pointer) instead of if(pointer == NULL):

It is simple, small
Less chances to write a buggy code, suppose if I misspelled equality check operator == with =
if(pointer == NULL) can be misspelled if(pointer = NULL) So I will avoid it, best is just if(pointer).
_{(I also suggested some Yoda condition in one answer, but that is diffrent matter)}
Similarly for while (node != NULL && node->data == key), I will simply write while (node && node->data == key) that is more obvious to me (shows that using short-circuit).
(may be stupid reason) Because NULL is a macro, if suppose some one redefine by mistake with other value.