Going to RPGBOT.net and looking at 5e, PHB races with classes that are listed as 'red' (worst option), not using the 'Customizing Your Origins' option (which improves many) include...
Dragonborn cleric, druid, monk, or rogue
Dwarf bard, sorcerer, or warlock
Gnome barbarian, cleric, druid
Half-orc artificer, cleric, monk, rogue, sorcerer, warlock, or wizard
Halfling artificer, barbarian, or wizard
Some of these sound kind of interesting from the fluff point of view...imagine a dwarvish bard quaffing ale and spinning epics of the monsters they've fought over the past 300 years, a dragonborn using the spikes on their body in battle, or the half-orc whose mom had a thing for green tusky guys and taught them wizardry...
Using the somewhat antiquated (2017) D&D race/class crosstabs from 538 (yeah, the politics site--https://fivethirtyeight.com/features/is-your-dd-character-rare/), the least common combo is the aasimar ranger, followed by aasimar wizard and druid. Least common combo for each race is aarakocra paladin, goliath wizard, gnome paladin, half-orc wizard, halfling paladin, genasi paladin, tiefling barbarian, dragonborn druid, dwarf sorcerer, half-elf barbarian, elf barbarian, and human druid. A lot of these seem more lore-counterintuitive than necessarily bad mechanically--a goliath wizard benefits from endurance, for instance.