Is the phrase "for free" correct?

This service is free.
The food is provided free of charge.
I got this item for free.

All the sentences are correct.

Reasonable paraphrasings of the word free in this context are for nothing/for no payment. Clearly the word "for" can't be omitted from those paraphrasings. Thus many people will say that for free equates to for for free, so they feel it's ungrammatical.

• How much does this cost?
• It's free.
• It's [available] for nothing.
• It's [available] at no cost.
• It's for free. (this usage sounds 'wrong' to many)

Many people use the expression (at least informally), so it seems futile to take issue with it - though more "careful" advertising copywriters do still tend to avoid it.

I don't know if it was David Crosby or Joni Mitchell who wrote the lyrics to He Played Real Good for Free that she sings so well, but I can't imagine dropping the word "for" there.

For free is an informal phrase used to mean "without cost or payment."

These professionals were giving their time for free.

The phrase is correct; you should not use it where you are supposed to only use a formal sentence, but that doesn't make a phrase not correct.

I believe the puzzle comes from the common but mistaken belief that prepositions must have noun-phrase object complements. Since for is a preposition and free is an adjective, the reasoning goes, there must be something wrong. The fact is that even the most conservative of dictionaries, grammars, and usage books allow for constructions like although citizens disapprove of the Brigade's tactics, they yet view them as necessary or it came out from under the bed. That is, they tacitly accept prepositions with non-object complements while claiming that all prepositions must be transitive.

A more coherent view is that prepositions, like nouns, adjectives, and verbs take a variety of complements. In the case of for, one of them is free.