The Nintendo 3DS XL is fully backward compatible with the vast majority of Nintendo DS game cartridges. You can simply insert a DS game card into the 3DS XL's slot and play immediately. The system emulates the DS hardware, rendering games at their original resolution on the larger screens (with optional scaling).
For 99% of the DS library—including heavy hitters like Mario Kart DS, Pokémon HeartGold/SoulSilver, The World Ends with You, and Castlevania: Dawn of Sorrow—the 3DS XL is an excellent way to play. You even get the benefit of save-state suspension via the Home menu and sleep mode.