Yes.
4 classes of emulation available for the DS family
1) Old GBA emulators if you have a GBA slot flash cart (or GBA emulator). Some of these have nice features, more polish than some DS efforts or handle some more obscure systems that never made it onto the DS.
2) Plain DS emulators.
3) DSi stuff. As you are not on a DSi though this does not count, and frankly other than the X86 emulator it does not make a great deal of difference.
4) Enhanced flash cart stuff. For most this means the DSTwo and versions thereof (the main other two options being the ISMM and iplayer, neither of which have as much as the DSTwo and anything vaguely exclusive they had has since been ported to the DSTwo). The DSTwo has onboard CPU and some other stuff so it can emulate quite a bit more than the stock DS. Most notable for most is the SNES emulator which does better than the plain DS efforts and the GBA emulator which is pretty playable, unlike the DS code GBA emulators which are more proof of concept than something you would want to use (especially if you can also get a GBA flash cart to use). The DSTwo has stuff baked into its kernel, plugins it can use and something called Dingux which has some emulators as well (technically including a PS1 but don't expect much more than about 17fps out of that one if the game works at all, enough for a puzzle game maybe but not going to be playing Final Fantasy, Crash Bandicoot or the like really).
It can get a tiny bit more fiddly -- some of the DS emulators can make use of the extra RAM from some GBA flash carts to do a tiny bit more, but nothing of great note as far as emulators. On the other hand said RAM does allow you to do better for Quake and is required for Quake 2
https://wiki.gbatemp.net/wiki/3_in_1_Expansion_Pack_for_EZ-Flash_V#Third-Party . Also there is a PCE/TG16 emulator that can make use of an old GBA flash cart to have a measure of CD support. Don't worry too much about that though.
There are better sites to read about things, and grab them (
https://www.gamebrew.org/wiki/List_of_DS_homebrew_applications , this site, this site's download section) but for 1) and 2) then the following makes for a decent overview to start with
http://nintendo-ds.dcemu.co.uk/emulators-for-gba-1158173.html
http://nintendo-ds.dcemu.co.uk/emulators-for-nintendo-ds-1158162.html
As a general rule anything common in the 8 bit era is probably OK, as are pre GBA handhelds. The genesis/megadrive does well enough, and PCE/TG16 on the GBA is not bad. Pre 8 bit stuff varies but you can do a lot. Sadly not much for the Amiga outside of some stuff if you smack a DSTwo hard enough. For anything with a keyboard try to go for the DS version.
I mentioned quake and quake 2 in passing above and it should be noted there are plenty of great ports, remakes and such available for both the GBA and DS, this in addition to the loads of original homebrew.
https://gbatemp.net/threads/links-to-various-gbatemp-features-over-the-years.352851/ mostly has some of the commercial games we covered but also notes ROM hacks, homebrew and such we liked enough to make more than news articles about.