Some fish, usually goldfish, and it seems at least some bettas and dwarf puffer fish and no doubt others, are particularly interactive. I do think it can depend on how much stimulation is provided to the fish, though.
Two of the goldfish I had were particularly interactive - neither belonged to me at first but others commented on how the first one seemed to be particularly interactive with me, while I didn't find the second one particularly interactive but developed a fondness for her, and I adopted each from the original owner. Over time, the second fish became as engaging with me as the first fish did, presumably because the stimulation I provided enabled that to happen. Both - in separate tanks - would behave in frenzied excitement as soon as they saw me enter the room and would "follow" me wherever I went in the room (not others), and would have "conversations" with me in that if I interacted with them by talking animatedly with them, they would "mirror" that behaviour back (ie moving around excitedly on the spot and opening and shutting their mouths quickly unlike in their usual state) when I paused doing so. The first fish would move to the location in the tank where particular foods were given and behave in an animated fashion, as though (and even my extremely sceptical husband was the first to notice and comment on this) telling me which type of food he wanted at that particular point in time. I used to feed him frozen food but stopped after he seemed to be at death's door for a week and could only put it down to a dodgy frozen food cube - 4 years later, I was struggling to get a paracetamol for myself out of a blister pack, and the goldfish started behaving in frenzied excitement, as though he recognised the sound as being associated with a food he used to love. This first fish also resided in the room where I often sat, working on my laptop late into the night; frequently, he would lift up and spit stones at the glass, in an effort to get my attention, and thereby get me to feed him (which, more often than not, I succumbed to doing). There are more examples I can cite but these are the most memorable.
I do miss these goldfish immensely and their interactivity. The tropicals are not the same in that regard but I do interact with them a lot, especially now that I'm at home most of the time. I do find that they "react" to their environment but don't "interact" to the same extent ie they will react when I approach the tank but I suspect wouldn't even try to encourage me to feed them if I somehow forgot, whereas the goldfish would do anything in their power to get fed, building up an ever-increasing frenzy. The tropicals have their own little world ie the company of one another and all that that entails which is good, but I'll "keep working" on them to encourage them to become more interactive.