What is the "Max current" for AWG#16?
The reason you're getting lots of different answers is that there is no hard maximum current a particular cable can handle since it depends on the application.

You need to specify what physical limit you don't want to exceed for your "maximum" criterion.  Do you want the wire not to rise above ambient temperature some amount?  If so, what amount?  If you can only tolerate a 10&deg;C rise, then the maximum current will be less than if you can tolerate a 50&deg;C rise, for example.  Or maybe the limiting parameter for your application is voltage drop, which could make the maximum current quite different again.

AWG #16 copper wire has a resistance of 4.016 &Omega; per 1000 feet, or 4.016 m&Omega;/foot, or 13.18 m&Omega;/m.  If you need to keep the voltage drop along 1 m of wire to 100 mV or less, then you can't push more than 7.59 A thru it.  If you need to limit the power dissipation to 1 W/foot, then you can't push more than 15.8 A thru it.  1 W/foot would get noticably warm, but should not be dangerously so for most uses.

If you are using it for house wiring, then it becomes a legal matter and you simply look up the answer.  One chart I looked at says the limit is 3.7 A for "power transmission".  That was chosen to be very conservative so that some amount of degradation and screwups can happen and your house is unlikely to burn down due to overloaded wiring.  Legal limits will vary by jurisdiction and which electrical code is being applied.  You will have to consult the electrical code that applies to your area and circumstance to get the answer.

That same chart that shows 3.7 A as the maximum for power transmission also shows 22 A maximum for "chassis wiring".  Presumably more temperature rise is acceptable inside a chassis.

So to get a straight answer, you have to tell us what you are really trying to do.  There simply is no inherent maximum current until you get to where the copper melts.  Even that depends on ambient temperature assumptions.