Hello! I would like numbers on:

- How many video games were released in 2003, 2004 and/or 2005?
- How many games were released on each platform? (XBOX, 360, PS2, PC,
Mac, PSP, GameCube, etc.)

These numbers can be approximated, but will need some data sources to back them up.

Thanks very much!

- How many video games were released in 2003, 2004 and/or 2005?
For the following platforms:
Gamecube, PC, Playstation 2, Playstation 3, WII, Xbox, Xbox 360, DS,
Gameboy Advance, PSP, Mobile, N-Gage, 3DO,

Dreamcast, Genesis, Jaguar, N64, Neo-Geo, PS One, Saturn and Snes a total of 
1909 titles was released in 2003,
1972 titles was released in 2004,
2089 titles was released in 2005.

- How many games were released on each platform? (XBOX, 360, PS2, PC,
Mac, PSP, GameCube, etc.)
2003
Dreamcast: 0
Game Boy: 0
Nintendo 64: 0
PC: 481
PS: 47
PS2: 265
Saturn: 0
Game Boy Color: 1
Genesis: 0
Gamecube: 145
GBA: 180
Xbox: 207
3DO: 0
Jaguar: 0
NeoGeo: 3
SNES: 0
Macintosh: 19
Sega CD: 0
N-Gage: 14

2004
Dreamcast: 0
Game Boy: 0
Nintendo 64: 0
PC:478
Playstation: 13
Playstation 2: 283
Saturn: 0
Game Boy Color: 0
Genesis: 0
Gamecube: 110
GBA: 166
Xbox: 195
3DO: 0
Jaguar: 0
NeoGeo: 0
SNES: 0
Macintosh: 2
Sega CD: 0
N-Gage: 19

2005
Dreamcast: 0
Game Boy: 0
Nintendo 64: 0
PC: 554
Playstation: 0 
Playstation 2: 298
Saturn: 0
Game Boy Color: 0
Genesis: 0
Gamecube: 101
Game Boy Advance: 175
Xbox: 229
3DO: 0
Jaguar: 0
NeoGeo: 0
Snes: 0
Macintosh: 7
Sega CD: 0
N-Gage 24

Source: http://www.gamerankings.com/itemrankings/simpleratings.asp
Adding the games per console doesn't yield the total amount of games
released in that year, I don't know why.
Gamerankings filter settings are somewhat limited, you can manipulate
them this way:

http://www.gamerankings.com/itemrankings/simpleratings.asp?max=<maximum
number of games show, choose something like

2500>&platform=<the number corresponding to the platform (see
below)>&range=<release year>

Platform numbers:

1	Dreamcast
2	Game Boy
4	Nintendo 64
5	PC
6	Playstation
7	Playstation 2
8	Saturn
9	Game Boy Color
10	Genesis
11	GameCube
12	Game Boy Advance
13	Xbox
15	3DO
17	Jaguar
18	NeoGeo
21	SNES
42	Macintosh
1002	Sega CD
1006	N-Gage

So if you want the statistics for the PC for the year 2004 you could use this URL:

http://www.gamerankings.com/itemrankings/simpleratings.asp?range=2004&max=2500&platform=5

Thanks very much for your research! 
I'm wondering though if searches on www.gamerankings.com only reflect
data for games that have been rated by one of the sites or magazines
that GameRankings monitors. I searched on all PC titles released in
2004 and came up with only 92, which seems very low to me.

Can I ask where you found these numbers? 
1909 titles was released in 2003,
1972 titles was released in 2004,
2089 titles was released in 2005.

Thanks!

"Can I ask where you found these numbers?"
Also from Gamerankings. There search function is limited to 200
results. However, you can get around this the following way:
Go to
http://www.gamerankings.com/itemrankings/simpleratings.asp
Select year, platform etc. The years I selected were 2003, 2004 and
2005. The platform was 'all'. Because the 200 limit the list will stop
after 200 games. Now, in your adress bar, add the following:

?max=2500

after

http://www.gamerankings.com/itemrankings/simpleratings.asp

and hit enter.

(So it will look like this: 
http://www.gamerankings.com/itemrankings/simpleratings.asp?max=2500)

This way, you can get a complete list of the games known to
gamerankings released in a certain year.

Good luck with your research.

I happen to know that there are about 260 Nintendo DS games out currently...