I have an extra car battery that I'd like to charge on a long upcoming drive. I have a spare cigarette lighter plug with ~16 AWG wire. If I use that to connect the battery to the cigarette lighter port, will that charge the battery while the car is running, or am I going to get too many amp flowing through the accessory circuit and blow a fuse?
If an adequate length, your 16AWG wire may provide adequate resistance to prevent blown fuse problems. If 10 feet long, it will be about 0.08 ohm. Longer may be better for this application.
To experiment, you may want to use an in-line fuse holder with a fuse value less than than of your car's cigarette lighter outlet (usually 15A). That way, if you do end up blowing a fuse, it's one that is easy to replace.
This is not really an advised approach for charging the battery. A car battery can demand a lot of charge current if the source can provide it. You will very likely blow out the accessory fuse if there is one in series with the lighter port.
Also the 16 AWG wire is not really a suitable gauge for charging a car battery. You should take a look at the size of the wire that is in your car from the alternator over to the battery and you will get a better idea of the more suitable gauge of wire used for this application.
Finally you have to consider the fact that any battery you attempt to parallel into the car electrical system will also try to feed back into the system when the system demands current draw such as when you try to start the car. Current flow in these conditions could exceed the current when you were attempting to charge the battery.
If you do intend to fix things up to support two batteries at once it is really important that you consider getting an automotive battery splitter (often available at RV supply outlets). These things generally consist of two diodes that feed from a common input terminal to a pair of output terminals. The high current lead from the alternator output feeds the splitter input terminal. One output terminal is used to feed out to the existing battery plus car electrical system. The other output terminal is used to feed to the secondary battery. The installation of such device gives you the basis to install the suitable heavy guage wire to the second battery. The diodes in the splitter solve the problem of back feed from the second battery back into the car main electrical system during cranking or low main battery conditions.
Depending on how discharged your battery is you either would not have any problems or would blow the fuse.
Use a resistor to limit the maximum current. Something like 0.1Ohm to 0.5Ohm would probably be OK.
Your battery will charge very nicely this way. But the second your car demands current from the main battery, your charging battery will attempt to provide around 50% of this current backwards through the cigarette socket which could burn out wiring, let alone the fuse. Get a proper battery charging kit as made for trailers and caravans. Leave the cigarette light for light current use only!