Dwarven Resilience, Darkvision, etc. Sure, humans can be miners and smiths, but the point of dwarves is that they were created to fulfill that niche (by Tolkien, the D&D game designers, and the in-lore gods in lots of worlds). They have a niche, and IMO, justify their existence in that. Halflings don't fulfill their niche as well as dwarves do, IMO.
Darkvision, innate spellcasting, damage resistances/immunities, powerful build, magic resistance/gnomish cunning, Small size, flying/climbing/swimming speeds, age ranges, Deathless/Constructed Nature, etc, etc, etc. I could go on and on. If you don't want just mechanical things, how about things like this:
- You were made out of metal to serve as war-slaves (Warforged).
- You're part animal (Centaur, Satyr)
- You're an anthropomorphic animal (Tabaxi, Leonin, Owlfolk, Aarakocra, Lizardolk, Rabbitfolk, Locathah, etc)
- You're half-(insert otherworldly/monstrous creature), and it changed your physical nature and granted you magical powers (Dhampir, Tiefling, Aasimar, Genasi, Hexblood, Kalashtar, etc)
- You came back to life, but not really (Reborn)
- You're half-(insert other race) (Half-Elf, Half-Orc, Mul, etc)
Be master tinkers/illusion-masters, not connected to Corellon, be curious and antisocial instead of haughty and xenophobic, etc.