Luigi Dude is right. I looked on Wikipedia, and it says the last GBA game in NA came out in February 2008. That's several YEARS after the launch of the DS back in late 2004. There is also a Metal Slug game listed on the Toys R Us website that might come out at some point.
But anyway, that shows the GBA had a life of 3+-4 years after its successor. The PS1's last game came out in 2004, which is 4 years after the PS2's launch in 2000. So maybe the PS1's life was a few months longer than the GBA's in that respect, but its close and the difference isn't worth mentioning.
BTW, the PS2 is still going. Not strong or anything, but its still seeing releases and still selling decently. It will be interesting to see how long it lasts. Can it beat the PS1's post-successor lifecycle of 4 years? Personally, I think it will because the PS3 adoption rate has been fairly poor.
But getting back on topic here, the DS's lifecycle will almost certainly be at least 4 years after the DS2. With sales going as strong as they are and with it still not dropping down to $99, it shows it still has a LOT of life left in it. The DSi was just released not that long ago, and its potential has barely been scratched yet. I predict it will have longer legs than the GBA and PS1.