From all that I have thought through and also searched online, there appears to be no way to do this.
The following workaround however should work pretty well.
Basically you will apply a label to emails that you have responded to, to someone and then search for those emails / conversations (via the Gmail online interface, Gmail adds labels to conversations) that don't have a label in order to see the ones you don't respond to. If however someone responds to you after you have issued your first reply, and you need to reply again, this won't be of any help to you since the conversation has been labeled already.
So, here are the steps: (This also works for emails you have already received. For future emails, you will only have to do Step 2 as Step 1 will automatically be done.)
1) Create a filter to label emails that have re: or fwd: in the subject that you sent to someone. Example: to:Bob subject:("re:" OR "fwd:")
We'll assume that the name of your label is Replied.
So, every time you reply or forward an email to Bob and don't edit the subject by removing the automatic Re: or Fwd from it that Gmail inserts in the subject, it will automatically be labeled Replied
2) Do a search for those emails by Bob that don't have the label you chose in Step 1. Example: from:Bob -label:Replied
Instead of using Bob, you can use his email address instead if you have several Bob's. Also, keep in mind, as I already said, if you respond to Bob and he then responds to you, and you need to respond to him again, but forgot or choose to do so later and then want to see / check if you responded to him a 2nd time, this won't be of any help to you.