Yes. The Nintendo 3DS (all models: Original, XL, 2DS, New 3DS, New 2DS XL) plays both Nintendo DS and DSiWare games natively.
For DS games: New 3DS XL / New 2DS XL — larger screens, stable 3D (irrelevant for DS), better battery, C-stick/ZL/ZR (unused in DS mode).
For DSiWare: Transfer before eShop closure. Otherwise, homebrew on CFW 3DS is only way to add new titles.