Yes and no. The DS has a homebrew system appropriately called nesDS and it will run 99% NES games. However, due to the DS' limited cpu power, it cant fully emulate SNES. Its choppy and slow, especially with sound. Even my 624mhz PDA cant run SNES at full speed. Im not sure what the limitation is because even an old AMD K6 700mhz runs it fine and the 200mhz Dreamcast can run it. Probably an architecture issue.
Lastly, a quick search over at gbatemp reveals if you have a DSi, only working slot-1 cards are the Acekard 2i and iM3.
Like I said, if anything if you have a regular DS, get a cycloDS or Acekard2i because most of the hot titles that are out are giving old cards trouble eg GTA Chinatown Wars and if the dev team isnt keeping up with firmware, you wont be able to play them. Im not sure where else to buy except dealextreme, though. They took a long time but they ship.