UPDATE:
Here are some more homebrew things I have found:
Colours!
This is essentially a paint program for the DS. The beauty of it is that it's pressure sensitive on the touch screen. So if you press lightly, you get a lightly coloured stroke.....press harder and you get darker colours.
This is the kind of picture you can end up "painting":
Also, once you've finished, the app will "playback" all your brushstrokes from the blank canvas to the completed picture so you can see it redrawn in front of you....brilliant fun (search for Colors DS in Youtube to get a whole load of example vids of it in action).
Gorilla DS
Basically this is Artillary Strike for the DS. Choose the angle and power of attack (taking windspeed into account) and guide your explosive bananas over the skyscrapers to the Simian on the other side

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Pong DS

This classic works brilliantly with the DS.
Does anyone remember a really addictive Win '95 game called Chips Challenge?
....well, someone's made a homebrew version for the DS:
Portabledev - Codename Hacker
It's been renamed
Codename Hacker, but is essentially the same game (and same method of writing down a 4 letter code in order to revisit that level

, and also has a few extra levels too.
Here is a screenshot:
Pocket Physics.
It is a homebrew physics simulator for the DS (basically a port of the minigame Crayon Physics).
You simply draw whatever shapes you want on the canvas....blue shapes are movable and red shapes are static.
After you've "set up" the scene, press play and watch everything interact under the force of gravity.
Sounds odd but is surprisingly addictive

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Here are some vids of it in action:
YouTube - Pocket Physics - Homebrew Physics Simulator for NDS
YouTube - Pocket Physics For NDS
Another great site full of homebrew roms is
PDRoms - News btw

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