Do all GBA games work on a DS?

I was just curious because my GBA broke down and my DSi doesn't play GBA games

I haven't encountered any problems with all my GBA games.

There are a couple obscure third party titles that don't work properly but all of the major first and third party titles work perfectly on a DS console

But Only GBA. Any Gameboys games before GBA will not work.

All compatibility issues are minor at worst. For example, I believe the motion sensing in Wario Ware is reversed or something due to the fact that you're inserting the cartridge "upside-down" but the game is still entirely playable.

The only outright incompatible games are few and far between, just take note of what Kingre said about GB and GBC games.

I think pretty much all GBA games work with the DS, but there could be a few minor issues with some games.