Civilization Food (100) Coin (100) Wood (100) Villagers Miscellaneous Units Possible Permutations Chance to start with only food, gold, or wood and nothing else 11.1%
Aztec 3 0 2 5 Warrior Priest Food + Nothing[1] Chance to start with only one random crate (food, gold, or wood)  33.3%
British 2 0 2 6 ---- Food + Gold Chance to start with 2 random crates (food + gold, food + wood, or gold + wood) 66.7%
China 2[2] 0[3] 3[4] 6 1 Goat, 1 Disciple (no random starting crates from map)[5] Food + Wood Chance that a food, gold, or wood crate is spawned 55.6%
Dutch 0 4 1 6 Envoy Gold + Nothing[6] Chance that either (food + gold, food + wood, or gold + wood) is spawned 22.2%
French 3 0 1 5[7] Native Scout Gold + Food
German 2 0 1 3[8] ---- Gold + Wood
India 1 0 3 6 2 Explorers Wood + Nothing[9]
Iroquois 2 0 2 5 Free Travois[10] Wood + Food
Japan 4 0 2 6 1 -2 Cherry Travois (5,000 food each), 2 Explorers Wood + Gold
Ottoman 0 0 3 6 ----
Portuguese 2 0 1 7 ----
Russian[11] 5 0 1 5 ----
Sioux 3 0 0 5 ----
Spanish 2 0 1 6 War Dog
Map Food (100) Coin (100) Wood (100) Other
Amazonia 0-1 0-1 0-1 Starts with a market
Andes 0-1 0-1 0-1 ----  
Araucania 0-1 0-1 0-1 Starts with llama at TC
Araucania (Frozen) 0-1 0-1 0-1 ----
Bayou 0-1 0-1 0-1 ----
Borneo 0-1 0-1 0-1 ----
California 0-1 0-1 0-1 Starts with sheep at TC
Carolina 0-1
2-3
0-1
1
0-1
1-3
----
Caribbean 0-1 0-1 0-1 ----
Ceylon 0-1 0-1 0-1 275 XP start, Catamaran
Deccan 0-1
3
0-1
2
0-1
2
----
Great Lakes 0-1 0-1 0-1 Also includes frozen version
Great Plains 0-1 0-1 0-1 ----
Himalayas 0-1 0-1 0-1 ----
Himalayas - Upper 0-1 0-1 0-1 ----
Hispaniola[12] 0-1
3-4
0-1
1
0-1
1
----
Honshu 0-1 0-1 0-1 Start with Dock wagon, , 2 fishing boats (Includes Regicide version)
Indochina 0-1 0-1 0-1 Starts with a monastery, saloon, or fire pit, can see all of coast
Mongolia 0-1
----
0-1
1
0-1
----
Starts close to easily defended Mongol Scout treasure.  
New England 0-1 0-1 0-1 ----
Northwest Territory 0-1 0-1 0-1 ----
Orinoco 0-1 0-1 0-1 ----
Ozarks 0-1 0-1 0-1 ----
Painted Desert 0-1 0-1 0-1 ----
Pampas 0-1 0-1 0-1 ----
Patagonia 0-1 0-1 0-1 ----
Plymoth 0-1
5
0-1
----
0-1
1
Starts with TC Travois / TC Wagon, 1 scout, 1 turkey scout, and 6 pilgrims.  
Rockies 0-1 0-1 0-1 ----
Saguenay 0-1 0-1 0-1 Starts with either a market, plantation, or livestock pen (farm as native)
Siberia 0-1 0-1 0-1 Start with outpost
Silk Road 0-1 0-1 0-1 300 wood, Starts with Market, Ottoman get 50XP start
Sonora 0-1 0-1 0-1 ----
Texas 0-1 0-1 0-1 Starts with 2 towers and a barracks (or war academy), 2 blockhouses, or 2 war huts.
Unknown 0-1 0-1 0-1 ----
Yellow River 0-1
1
0-1
1
0-1
2
Starting crates seem to be bugged.  
Yucatan 0-1 0-1 0-1 ----
Yukon 0-1 0-1 0-1 ----
Miscellaneous Notes:
1 Every map adds random crates in addition to the base supply, but the addition is the same for every civilization.  Thus, if a map adds a +1 food and +1 coin crate, every player receives these crates in addition to the base supply.  It seems a maximum of 2 crates will be supplied (never 1 of each but have not verified).  China does not receive this bonus.  
2 The way the randomization works is assumed to be as follows:
Each player (on most maps) is guaranteed to receive 1 random resource crate (coin, food or wood).  After that crate is randomly selected, another crate will be randomly generated.  If the next crate generated is the same as the first, it will not spawn.  Therefore, there are 9 possible permutations (see the possible permutations above to the right).  
3 There are additional resources on the following maps (additional to the 0-1 of each resource usually spawned):
Carolina:  200-300 Food, 100 Gold, and 100-300 Wood Deccan:  300 Food, 200 Gold, and 200 Wood  
Hispaniola:  300-400 Food, 100 Gold, and 100 Wood Plymoth:  500 Food, 100 Wood
Yellow River:  100 Food, 100 Gold, and 200 Wood  
4 In addition, each civilization has different qualities of explorers and some receive bonus starting units (French Scout, Dutch Envoy, Spanish war dog, etc.).
5 The map script files are located in the following directory:  C:\Program Files\Microsoft Games\Age of Empires III\RM3 (not in the \My Games\Age of Empires 3\RM3 folder).  
6 See the Worksheet "Map Summary" for a detailed description of each map and more starting conditions such as outlaws, mercenaries, etc.
7 The crates generated as standard startup resources can be distinguished from those generated by the map script, at least for Native and Asia civilizations, as the map-created ones feature "European" art. 

[1]
NOTE:
Cannot spawn the same resource twice. 
[2]
NOTE:
Here are the relevant entries for the Chinese:

<townstartingunit>CrateofFood</townstartingunit>
<townstartingunit>CrateofFood</townstartingunit>
<townstartingunit>CrateofWood</townstartingunit>
<townstartingunit>CrateofWood</townstartingunit>
<townstartingunit>CrateofWood</townstartingunit>
<randomstartingunits>0</randomstartingunits>
[3]
NOTE:
Here are the relevant entries for the Chinese:

<townstartingunit>CrateofFood</townstartingunit>
<townstartingunit>CrateofFood</townstartingunit>
<townstartingunit>CrateofWood</townstartingunit>
<townstartingunit>CrateofWood</townstartingunit>
<townstartingunit>CrateofWood</townstartingunit>
<randomstartingunits>0</randomstartingunits>
[4]
NOTE:
Here are the relevant entries for the Chinese:

<townstartingunit>CrateofFood</townstartingunit>
<townstartingunit>CrateofFood</townstartingunit>
<townstartingunit>CrateofWood</townstartingunit>
<townstartingunit>CrateofWood</townstartingunit>
<townstartingunit>CrateofWood</townstartingunit>
<randomstartingunits>0</randomstartingunits>
[5]
NOTE:
On almost all maps, China receives the same amount of resources on startup regardless of what bonus crates are spawned on the map. 
[6]
NOTE:
Cannot spawn the same resource twice. 
[7]
NOTE:
Courier settlers:  Gather 25% faster, walk faster, and fight better
[8]
NOTE:
Settler Wagons (work twice as fast as settlers)
[9]
NOTE:
Cannot spawn the same resource twice. 
[10]
NOTE:
This discovery travois cannot construct Trading Posts or War Huts. 
[11]
NOTE:
Russians have the most overall resources, but it is required since  villagers are trained in batches of 3 (270 food).
[12]
NOTE:
From the Hispaniola.xs file:

 //Prepare to place player starting Crates (mostly food)
 int playerCrateID=rmCreateObjectDef("starting crates");
 rmAddObjectDefItem(playerCrateID, "crateOfFood", rmRandInt(3,4), 4.0);
 rmAddObjectDefItem(playerCrateID, "crateOfWood", 1, 6.0);
 rmAddObjectDefItem(playerCrateID, "crateOfCoin", 1, 7.0);