The VG Resource

Here you can find a number of tools: http://altmer.arts-union.ru/3DO/3do_utils.htm
unCD-ROM v1.2 will allow you to extract 3DO roms,
RIPto2048 will allow you to convert roms, unextractable with unCD-ROM by defaut, to extractable format
3DOResExplorer will allow you to view images and convert them to .bmp format, though isn't finished and will probably never be. Fortunately the source code is available to download so it may give some info about the 3DO file formats.
Also here is a Noesis plugin that I made: 3DO_CCD_texture_dumper
It allows you to rip .cel images, viewable by 3DOResExplorer, from various archives similar to how Gitmo works. Just open the plugin in a text editor like notepad and replace ".pak" in the line handle = noesis.register("Dump 3DO CCD images", ".pak") with the format you want to rip sprites from and open the file in noesis. It is not finished and will probably be updated later. Also for some reason it won't work correctly unless you reload plugins after every extraction and unfortunately I don't know what's causing it.
Game specific info:

TIM2 (.tm2) format is commonly used for sprites and textures in PS2 games. Unfortunately, just like with the Dreamcast's .PVR, I've never seen a list of games using this format. I only know that Final Fantasy XII and Ikki Tousen: Shining Dragon use it for sure. Apparently there is also a TIM3 format, but I've never encountered it myself.
Here is a simple Noesis plugin I made to extract .tm2 files from various archives: TIM2_dumper
It works similar to the 3DO_CCD_texture_dumper, except you don't need to reload plugins every time, so please refer to 3DO section for information on how to use it.

Noesis supports a number of standart Dreamcast image formats (.PVR, .PVM, maybe more). From what I've seen so far the .PVR format is very common, in fact every Dreamcast game aparently has at least one .PVR image (disk cover). It is possible that many games store sprites entirely in .PVR but unfortunately there doesn't seem to be a list of them yet.
Game specific info: