What is correct: “crave” or “crave for”?

You would normally say “I crave an apple pie”, and not “I crave for an apple pie”.

One definition of the verb “to crave” is “to have a great desire for”. If you were to say “I crave for an apple pie” you would be saying “I have a great desire for for an apple pie”. You don’t need the extra “for”.

There are two other things you might want to know.

One is that “crave” sounds a bit old-fashioned now. It’s a good word to know, but “I really want an apple pie” might be more usual in everyday speech.

The second is that there is a noun: “craving”. This is still used a great deal – and it’s followed by “for”. You can say “I have a craving for apple pie”. Pregnant women often have irresistible desires for particular foods. These are called cravings. They might say “I have a craving for raspberries” or “I have a craving for cheese and onion crisps”. Then their partners have to go searching for raspberries, cheese and onion crisps or whatever at all times of day and night.

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_{With thanks to Elizaveta for the question}