Is it ok if I use "that" in the following sentences?
He promised he that he will come tomorrow / He promised he will come tomorrow
I think that he is crazy / I think he is crazy

Question

Answer

Your first sentence has an extra "he" in it. Otherwise, all of the sentences are acceptable with or without "that." 
Here's a discussion about when you can omit "that": http://www.usingenglish.com/forum/threads/65757-Include-or-omit-quot-That-quot

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