You can use any of them, depending on what you mean.
I hope (just now, in the recent past) I didn't offend you.
I hope (looking back on my past actions) I haven't screwed this up.
I hope (right now) she likes the proposal I just made.
I hope (tomorrow) that the weather will be nice.
I hope (in the indefinite future) my children will make good choices.
- For Teachers