SNES - you have 2 options, SNES DS and SNEmulDS. Of these, SNEmulDS is highly recommended. Instructions for both can be found at their respective articles on http://wiki.pocketheaven.com - for SNES DS, follow the "quickstart slot-1" instructions and/or the video tutorials I made, and for SNEmulDS just follow the instructions on the page. For patching with DLDI, using the "DLDIrc" tool is recommended for its ease of use. Just install it and then right-click the .nds file to select the new patching option.
With SNES DS, you'll have to package the game into the .nds file, whereas SNEmulDS reads .smc files straight off your media card.
Megadrive/Genesis - only option is PicoDriveDS, which you can find via Google. Patch it with DLDI and then place your *.bin files anywhere on the card. Note that this emulator is rather slow, has a forced frameskip, and has no sound. It does however have several screen scaling options and the ability to have one savestate per game.
SMS - I think the best one is DSMasterPlus. I've heard the SMS emulators for the GBA are more refined, but you can't run them on an R4.
N64 - will never happen on a DS, sorry. The DS is way too underpowered to emulate something like that.
GB/GBC - search for Lameboy, which is up to version 0.6 at this moment. It has no sound, and doesn't limit the frames so some games will run faster than usual, but it's a good start. I'd recommend downloading a few versions so that you can use an earlier, slower version if the latest one runs your game too fast. Again, Goomba Color for the GBA is much more polished, but Lameboy is your only option on the R4.
Other systems - http://www.portabledev.com/pages/ds/nds-emulation.php
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