There are many water conditioners on the market. You specifically asked about water conditioners that neutralize ammonia -- that IS unusual -- Prime is one of very few that do that.
Most of the available ones will neutralize chlorine and chloramines. Many of the high-quality ones will neutralize heavy metals. Ammonia is the kicker. If you have tap water that contains ammonia (you'll need a liquid testing kit to determine that), then you will want something like Prime whether your tank is cycled or not, as it neutralizes ammonia almost instantly, whereas the bacteria in your tank (if it is cycled) will some time to metabolize it. Otherwise, you're adding ammonia to your tank water every time you do a water change!
Stress Coat+ is probably the second-most popular conditioner here. It does everything Prime does EXCEPT the ammonia. You can even get it in some stores in a tiny flip-top bottle. I refill mine from a bigger bottle so I can measure it out accurately.