Ah yes, the world of DS homebrew, what a wonderous world it is.

My bet is that most of you here are completely oblivious to what that is, let me explain.
"Homebrew" refers to games or programs that have been created by hobbyist programmers, specifically for games consoles, in this case, for the DS.

You're probably now wondering, "Wait, how do I even play homebrew on my DS"? Easy, with a flash cart of some sort.
There exist multiple flash carts out there for the DS that can store your homebrew games and play them, I personally use one called R4DS because of how easy it is to use.
The flash carts are also usable for piracy, but I don't recommend, nor do I condone it.
If you don't own a DS, or a Flash cart, you can use DS emulators such as no$gba to emulate the homebrew, remember that emulators are entirely legal.

So, now that you're educated about the wonderful world of DS homebrew a little, why do I love it? Let me show you some prime examples.

GAMES:

WORDUP:
A favourite game of mine, this puzzle game features a field of letter blocks falling from the sky, and you have to touch the letters and make words out of adjacent letters, with a good vocabulary you'll get great at this game, and you'll even remember or learn some words.

MartianDS:
MartianDS is a game similar to Alien Hominid, it's a short game that was programmed in just 72 hours and only features 2 levels, but it surprisingly enjoyable to play with interesting artwork, a good weapon system, funny sound effects that were done with voices and a fantastic donut huffing boss.
Sadly, no music.

POPULATION: TIRE:
Homestar Runner fans will like this, this is a straight from Flash game to DS homebrew port of the tire bouncing game, basic aim is to not let the tire touch the soil for as long as possible, it's fun, try it out.

PROGRAMS:

PHIDIAS:
Phidias is a brilliant drawing application that offers a wide colour pallet, brush support, saving and loading and blur/smudging with brush size and pressure, you can paint some real nice images if you take the time and later, take the images from memory and upload them to your computer.

MOONSHELL:
This homebrew is so brilliant that some flash carts even come pre-loaded with the software.
It's a simple yet powerful media player that supports MP3s, OGGs, many Video Game music files including SPC for SNES music, DPG files (Video!), as well as text files for reading and image files for viewing, ideal for downloading some game guides to take with you on the road.
With a nice storage capacity, you can put some videos and music on it and replace your iPod nano, hell, you can pretty much put any youtube video on here if you know how!

BEUP LIVE:
I don't get to use this one often because it requires a wireless internet connection, and my Nintendo Wifi USB connector is only compatible with official DS games.
So what it is? It's MSN, or Live Messenger, right on your DS! It's fully compatible with your contacts list and has a great interface, complete with your display pictures and apparently even supports drawing! I've only used it once but it is highly recommendable.

DSORGANISE:
As the name implies, this gives your DS full Organiser functionality, including to do lists, text editors, scribble pads, calendar and even a simple web browser.

COMICBOOKDS:
This program is great for all of you who read a lot of comic books, with the use of a PC application to convert a zip file of comic book pages into a .cbds file, you can then read the .cbds files on your DS using this program, I've used it for a couple of Phoenix Wright mangas and it works very well. :)

EMULATORS:

LAMEBOY:
Lameboy is a Gameboy and Gameboy Color emulator which runs at great speed most of the time and has good compatibility as of right now, it features gamesave support, great sound, fake-bilinear upscaling, and even REAL TIME CLOCK, which means you can play Pokémon Gold Silver and Crystal with the clock working and everything! It also has speed up with the L button.
Right now, I'm playing Zelda: Ocarina of Ages on this and loving it.

jEnesisDS:
jEnesisDS is a good speed Genesis/Megadrive emulator for the DS, although the speed is inconsistant and no sound exists right now, this is a recent big step forward in DS emulation for this console. Still early, there is a lot of hope for this emulator in my opinion.

NESDS:
Gee, I wonder what this is?
Oh right, it's NES games on your DS. :P
It runs at full speed and features great scaling options to fit on the DS screen, additionally it supports savestates, fast forwarding, REWINDING and autofire, making this a highly recommendable emulator.
Not all games work, for example Punchout because of different NES mappers, but you'll be happy to hear that all Megaman games will work. :)

SNEmulDS
This would be a SNES emulator, it works fairly well with good speeds and good sound, there still a lot of work to be done but you can even emulate Mario Paint successfully.
Problems with layer ordering exist right now, and scaling does not exist, hopefully these will come later, but for the time being Super Mario All Stars and Super Metroid work great.

Do you see now the ever expansive world of DS homebrew? This is only a small sample of what you can get for your DS, it's all free too! New content is always being created and updated, if you really love what they've developed, maybe you should even consider a donation or two, I've already donated a little to Lameboy. :)