Acceptable Screenshot Resolutions

Amiga
The Amiga is notorious for changing the screen size between, or inside, games. Look out so that you don't crop overscan areas, since some games exceed the default PAL and NTSC resolutions. Do not use GIF for Amiga screens, unless you are absolutely certain that less than 256 colours are used, including rainbow effects in the background. PNG is the preferred format.
 * 320x200 / 320x400 / 640x200 / 640x400 NTSC
 * 320x256 / 320x512 / 640x256 / 640x512 PAL

Apple II

 * 560x384 / 280x284 color png/gif

Apple IIgs

 * 320x200 / 640x200 png/gif

Amstrad CPC

 * 320x200 png/gif
 * 384x270 (overscan)
 * 640x400 (hi-res)

Atari 8-bit
Being the predecessor of the Amiga, the Atari 8-bit computer is also prone to change the size of the screen. The above resolution should capture all the overscan area, but cropping is welcome if you get big borders at that resolution.
 * 336x240 png/gif

Atari ST

 * 320x200 / 640x400 png/gif

BBC Micro

 * 320x256 (low-res)
 * 400x300 (emulators, using overscan)
 * 640x250 (mode 7)

C128

 * 320x200 (40 column mode)
 * 640x200 png/gif
 * 640x400 (interlaced)

C64

 * 320x200 png/gif
 * 384x271 (overscan PAL)
 * 384x265 (overscan NTSC)

Dragon 32/64

 * 256x192 png/gif

MSX

 * 256x192 (16 colors)
 * 512x212 (16 colors out of 512)
 * 256x212 (256 colors)
 * 256x212 (19268 colors)

TI-99/A4

 * 256x192 png/gif

VIC-20
VIC-20 screen size varies a lot, just make sure that the aspect ratio is correct (pixels are usually twice as wide as they are tall) and that borders are not larger than necessary.

Windows

 * 320x200 / 320x240 / 640x400
 * 640x350 / 640x480 / 720x384
 * 800x600 / 1024x768 / 1152x864
 * 1280x1024 / 1600x1200

ZX Spectrum

 * 256x192 png/gif

Atari 2600

 * 320x200 / 320x225 / 320x240 png/gif

Atari 5200

 * 336x240 png/gif

Atari 7800

 * 320x200 / 320x225 png/gif

ColecoVision

 * 256x192 png/gif

Dreamcast

 * 640x480

Genesis/Mega Drive

 * 320x224 / 256x224

Intellivision

 * 320x200 png/gif

PlayStation 2

 * 640x480

PlayStation 3

 * NTSC 640x480 (4:3) / 720x480 (4:3) / 854x480 (16:9) / 1280x720 / 1920x1080
 * PAL 720x576 (4:3) / 1024x576 (16:9)

Sega 32X

 * 320x224 / 256x224

Sega CD

 * 320x224 / 256x224

Sega Master System

 * 256x192 gif/png (almost all games)
 * 256x224 / 256x240 gif/png (used in Codemasters games)

Vectrex

 * 360x480 png/gif

V.Smile

 * 640x480

XBox

 * 640x480 / 1280x720 / 1920x1080

XBox 360

 * NTSC 640x480 (4:3) / 720x480 (4:3) / 854x480 (16:9) / 1280x720 / 1920x1080
 * PAL 720x576 (4:3) / 1024x576 (16:9)

DS

 * 256x384

Game Boy

 * 160x144

Game Boy Advance

 * 240x160

Game Boy Color

 * 160x144

Super Game Boy

 * 256 X 224

Game Gear

 * 160x144

Neo Geo Pocket

 * 160x152

Neo Geo Pocket Color

 * 160x152

PSP

 * 480x272

Virtual Boy

 * 384 x 224