Kind of / sort of etc

The article a/an is usually left out after kind of, sort of, type of and similar expressions.

Have you got a cheaper sort of stereo? (More natural than … a cheaper sort of a stereo.)
What kind of person is she?
Scientists are developing a new variety of tomato.

After amount / number etc

We do not use the after the amount / number of.

The number of unemployed is rising. (NOT The number of the unemployed …)

Man and woman

The singular countable nouns man and woman can be used in a general sense without articles.

Man and woman are created equal. (NOT The man and the woman are created equal.)
Man is mortal.

Note that in modern English we often use the plural form men and women.

Men and women are created equal.

Exclamations

A/an is used with singular countable nouns in exclamations after What.

What a nice present! (NOT What nice present!)
What a lovely song! (NOT What lovely song!)

Note that a/an cannot be used with uncountable nouns in exclamations.

What nonsense! (NOT What a nonsense!)

Jobs and positions

The is not used in titles like Princess Diana, President Kennedy or Queen Elizabeth.

Compare:

Queen Elizabeth had talks with President Clinton. (NOT The Queen Elizabeth had talks with the President Clinton.)
The President had dinner with the Queen. (NOT President had dinner with Queen.)

Complements

The is not usually used with the complement of a sentence.

Compare:

He is the monitor. (NOT He is monitor.)
They appointed him monitor. (NOT They appointed him the monitor.)
He was elected Chairman. (NOT He was elected the Chairman.)
I want to talk to the Chairman. (NOT I want to talk to Chairman.)