1) If "crave" is used as a verb, do not use "for".

Wrong: "I crave for ice cream."
Right: "I crave ice cream."

If "craving"is used as a noun, use "for".

Right: "I have a craving for ice cream."

2) If "request" is used as a verb, do not use "for".

Wrong: "I request for office supplies."
Right: "I request office supplies."

If "request" is used as a noun, use "for".

Right: "Did you receive my request for office supplies?"