In terms of racial features? Quite a lot, actually. You're going to see the rogue pop up alot because...they're one of the most utility martials. Monks also have good utility.
A lightfoot halfling rogue's naturally stealthy feature mixes well with their cunning action, letting them essentially guarantee being hidden every turn as a bonus action by virtue of being near their allies and hiding behind them. A wizard can't just bonus action hide and I'm unfamiliar with any spell that let's them replicate that feature of the rogue.
Not only do any additional skills from race/background become a potential expertise target for a rogue, but they synergize with Reliable Talent. While a wizard taking a racial proficiency means they get a maximum of +11, the rogue picking the same option gets a bonus maximum of +17 with a lowest roll being a 27. Not to mention, certain races have tool proficiencies that act as expertise under certain conditions that will also gain the Reliable Talent benefit, like the gnome's Artificer Lore.
A wood elf's Fleet of Foot is a great way to give a monk a bit more distance with their extra movement and potential bonus action dash. A wizard might not need to move around the battlefield or moving along surfaces or liquids as swiftly depending on their gameplan. But also, the Fleet of Foot Barbarian gives the eagle totem a 45ft fly speed, 90ft in a dash. And this isn't a regular leap, either. This is a free 90ft flight. Meaning a barbarian can even maneuver in mid-air while moving in the air. A wizard getting an extra 5ft movement doesn't affect as much, especially since they usually want to be at range.
A shadow monk can get an extra casting of Darkness for free as a Drow. Considering the shadow monk wants to mainly be in darkness, them having 120ft darkvision is beneficial especially for seeing hostile creatures before they see the party.
Funnily, a barbarian with Aspect of the Eagle and a race with darkvision can pretty much see normally even in pitch darkness because dim light doesn't impose disadvantage on perception checks. I don't know of a wizard spell that can replicate this either.