First let's eliminate confusion. Indexes has the same meaning as Indices, and it's the plural of Index.
A stock market index is a basket of shares(stocks) designed to track market price changes.
Each stock market index has its own methodology for calculating the effect of changes in individual index components. 
Most stock market indexes uses capitalization-weighted adjustments to account for the differences in company size.

Indexes can track market characteristics instead of market values, for example, the Volatility Index (VIX) measures options premium to determine the market's expectation for future volatility.

There are also economic indices that track and measures the economic health, such as the Consumer Price Index (CPI).


The most popular Americas market indexes:

Index name	Yahoo Symbol	Components	Country
Dow Jones Industrial Average	^DJI	30	US
Dow Jones Transportation	^DJT	20	US
Dow Jones Utilities	^DJU	15	US
Dow Jones Composite	^DJA	65	US
NYSE Composite	^NYA	1652	US
NYSE International 100	^NIN	100	US
NYSE World Leaders	^NWL	200	US
Nasdaq Composite	^IXIC	3937	US
Nasdaq 100	^NDX	153	US
Nasdaq Banks	^IXBK	978	US
S&P 500	^GSPC	500	US
S&P 100	^OEX	100	US
S&P 400 MidCap	^MID	400	US
S&P 600 SmallCap	^SML	600	US
Major Market	^XMI	20	US
Russell 2000	^RUT	2000	US
Philadelphia Gold & Silver	^XAU	32	US
S&P 500 Volatility Index	^VIX	500	US
CBOE NASDAQ 100 Voltility	^VXN	153	US
S&P TSX Composite	^GSPTSE	60	CANADA
MerVal	^MERV	17	ARGENTINA
Bovespa	^BVSP	66	BRAZILIA
IPC	^MXX	37	MEXICO

The most popular Europe stock market indexes:

Index name	Yahoo Symbol	Components	Country
FTSE 100	^FTSE	100	UK
DAX 30	^GDAXI	30	GERMANY
CAC 40	^FCHI	40	FRANCE
Swiss Market    SMI	^SSMI	20	SWISS
Stockholm General	^OSEAX	610	SWEDEN
Madrid General	^SMSI	-	SPAIN
OSE All Share	^OSEAX	182	NORWAY
AEX General	^AEX	25	NETHERLAND
BEL-20	^BFX	20	BELGIUM
ATX	^ATX	20	AUSTRIA
EURO-STOOX 50		50

The most popular AsiaPacific stock market indexes:

Index name	Yahoo Symbol	Components	Country
All Ordinaries	^AORD	489	AUSTRALIA
NZSE 50	^NZ50	50	NEW ZEALAND
Nikkei 225	^N225	225	JAPAN
Hang Seng	^HSI	45	CHINA
Shanghai Composite	^SSEC	-	CHINA
Straits Times	^STI	30	SINGAPORE
KLSE Composite	^KLSE	30	MALAYSIA
Jakarta Composite	^JKSE	376	INDONESIA
Taiwan Weighted	^TWII	-	TAIWAN
Seoul Composite	^KS11	765	SOUTH KOREA
BSE 30	^BSESN	30	INDIA