Have you ever heard of a DS emulator called no$gba? With some recent developments, DS emulation has become really good.
It still requires a reasonably powerful machine to emulate a DS game well, but actual playability is very much in site now!
Problems still exist naturally, 3d games suffer slowdown (but very little of it with the latest developments) transparency sometimes messes up (it can be a hinderance in Picross) and 3d models don't display properly (shadows just don't work right.) But these are all gradually coming together, why, with the previous update, Megaman ZX would crash and Mario Kart was painfully slow! The biggest problem that exists right now is sound, many games sound fine, but going back to Mario Kart DS sound can be horrible.

Here's a list of games I've tested, keep in mind I've got a lotta ram, a powerful processor and a high-end graphics card on Vista.

New Super Mario Bros:
YES! Game is fully playable, intro has weird transparent sprites, slowdown with multiple 3d models is minimal!

Zoo Keeper:
YES! Infact, it's practically perfect

Brain Age:
WELL, it certainly works perfectly, except the emulator needs an option to rotate the screen sideways. :p

Megaman Starforce Dragon:
NO, 3d models just do not appear in battle...

42 All Time Classics:
NO, it never seems to get past the saving screen, and it still horribly slow and sounds awful.

Mario Kart DS:
YES! The slowdown is minimal and fully playable, but you'll need to put up with some bad sound quality.

Megaman ZX:
YES! Works great, even the videos they included, but there are some minor transparency issues.

Sonic Rush Adventure:
YES! The game plays amazingly well! The intro is a bit slow, the main levels work 100%, the boss battles are a bit slow, the Jet Bike levels work fine but have some bizarre graphical errors, but it's completely playable.

Megaman Battle Network 5 DS:
Maybe? The game works great, minor transparency issues, but I can't seem to save it, I can't be bothered to investigate, probably requires savetype configuration.

Zelda Phantom Hourglass:
YES? Now this is an odd one, during gameplay, it actually runs FASTER than it should.
I think I have an explanation for this too, when looking for action replay codes, it seems that this game has a built in V-sync option, disabling it makes the game go way faster than it should.
There's also a lot of shading issues and slowdown in some circumstances.
So it won't be easy playing with your mouse.

Tetris DS:
YES! It's fully playable and great speed, but one issue is that the background is not translucent, making it hard to see tetris pieces.
I prefer Tetris DX anyway, I hate 20g and infinite spin.

Animal Crossing DS Demo:
NO, the outdoors 3d models just don't appear, at all.

Pokémon Diamond:
YES! It runs at a great speed and such, although some graphic errors like water appearing black occur. Otherwise, fully playable!

So there you have it, these are the games I've tested, you can see, problems to exist but these should not be hard to overcome.
I look forward to what future developments the no$gba team makes, I might even donate if I can make use of it. :)