"Thought you'd never ask" is "I thought you'd never ask" with "I" omitted.
"Hope this helps" is "I hope this helps" with "I" omitted.
In English grammar, normally every sentence should have a subject, right?
My first thought is that these two examples are so often used that they are like set phrases. But these are not really set phrases. You can alter the words after "thought" and "hope".
Another possible explanation is the tendency to drop the subject if it is the first person pronoun. It seems that in many languages, such as Spanish, Italian and Japanese, the first person subject is usually omitted. Maybe English is going the same way? (Not exactly the same, since in Italian, verb forms change according to the person, so the subject is not necessary to understand who one's referring to.)
And, apparently, such omission is more common in spoken English than in written English.
Are there more examples of such first person subject omission? How frequent is it?