1. Mike doesn't often watch TV.
2. Mike often doesn't watch TV.
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Which one is grammatical? Are both OK? Which one is commonly usd?
The better of those is #1.
Often modifies watch; so being nearer to that word makes the sentence flow better.
Both sentences are grammatically correct, but they have slightly different meanings and patterns of usage.
1. "Mike doesn't often watch TV." - In this sentence, the adverb "often" is placed before the auxiliary verb "doesn't." It means that Mike does not watch TV frequently or regularly.
2. "Mike often doesn't watch TV." - In this sentence, the adverb "often" is placed before the main verb "doesn't." It signifies that there are times when Mike chooses not to watch TV, even though he usually does.
In terms of common usage, Sentence 1 is more typical and frequently heard. It follows the usual pattern of placing the adverb before the auxiliary verb in negative sentences. However, Sentence 2 is also grammatically correct, but it may sound less common or slightly less natural in some contexts.