UPDATE The formula has changed as of the March 2011 patch, it is now
(city population * 1.1) + (capital population * .15) - 1 for each city connected to the capital, not including the capital.
- The Machu Pichu wonder increases the modifier by 20%, to
(city population * 1.3) + (capital population * .15) - 1.
- Arabia increases the constant by 1, to
(city population * 1.1) + (capital population * .15) (thanks WillfulWizard).
The economic overview also gives a far better explanation of how it is calculated - in other words, this question is now trivially solved by simply looking at that economic overview :)
Original answer below.
Okay, I did a bit more testing, and bwarner's answer is almost accurate:
Each city, excluding the capital, provides (city's population * 1.25) + 0.01 gold per turn. Owning the Machu Pichu wonder increases the modifier by 20%, to (population * 1.5) + 0.01, for all the cities.
The capital does not provide any gold.
The 1.25 and 0.01 can be seen in the Assets\Gameplay\XML\GlobalDefines.xml file:
<Row Name="TRADE_ROUTE_BASE_GOLD">
<Value>1</Value>
</Row>
<Row Name="TRADE_ROUTE_CAPITAL_POP_GOLD_MULTIPLIER">
<Value>0</Value>
</Row>
<Row Name="TRADE_ROUTE_CITY_POP_GOLD_MULTIPLIER">
<Value>125</Value>
</Row>
The economic overview also demonstrates these values.
I couldn't find any other factor which affects these values, and I checked different difficulty levels, different distances between cities, different city route type (road vs railroad, road/railroad vs harbor), different city health and whether it is occupied. Looks like it's solely the population.
Best Answer
So based on Fabian's answer here combined with Oak's experience mentioned in the comments for this question, it sounds like razing a city will cause all tiles that were acquired by that city to become neutral, as well as all tiles in the immediate ring around that city, even if those tiles were not initially acquired by the city being razed (beacuse as Fabian pointed out, building/capturing a city will automatically transfer ownership of tiles in that inner ring that belong to other cities of the same player to the "new" city). Any tiles in the inner ring that do not belong to the player owning the city should not become neutral.
Unfortunately, I am not aware of any way to determine ahead of time which city initially acquired a tile and thus "owns" it for purposes such as this.