I did a quick scan of this thread and tried to consolidate these...
Dwarf:
* Diggers
* Stump
* Quasim
* Hairball
* Muckers
* Barrels
* Beardless
* Comparision to anything inactive and/or pointless
* Sunlover
* Toolbreaker
* Mudgrubber
* Barrel
* Beardy
* Santa
* Rock-boy
* Minor
* Goldies
* Cellar-dweller
* Grit-sucker
* Dirt-eater
* Shorties
* Bearded goblin
* hairy stinker
* Bath-hater
* Meat shield
* Clumsy
* Any made up word to represent another language
Elf:
* Pointers
* Dandelion eaters (Daisy eater, or other plant, etc)
* For males, effeminate versions of name; for females, other female names
* Fop
* Pointy-Ears
* Pointy-ear wuss
* Dandies
* Treehugger
* Grasseater
* Leaflicker
* Berryboy
* For elves that breed with humans, Sullier
* Oathbraker
* Wood baby
* Fairy
* Peg (Pointy Eared Git)
* Dancer
* Prancer
* Vegetable
* Sissy
* Fairy Princess
* from underdweller, surface dweller
* Any made up word to represent another language
Half-Elf:
* Half breed
* Mule
* half-man
* Fairyboy
* Wood baby
* Booze-baby
* Screwup
* Hermy (short for hermaphrodite)
* from underdweller, surface dweller
* Any made up word to represent another language
Orc:
* Snout-face
* Groin
* Slopes
* Feeders
* For orcs that breed with humans, sullier
* tuskers
* Any made up word to represent another language
Half-orc:
* Half breed
* Mule
* Snout-face
* Groin
* Slopes
* Booze-baby
* Feeders
* Screwup
* Any made up word to represent another language
Gnome:
* Minus
* Mudboy
* Rootsucker
* Garnder
* Duck
* Flighter
* Tink
* Noser
* Any made up word to represent another language
Halfling:
* Peck
* Shorty
* Leg (how tall a halfling is to a human)
* Fatty
* Woolies
* from underdweller, surface dweller
* Any made up word to represent another language
Human:
* Perv
* Breeder
* Stinker
* Pinkies
* For dwarf-likers, Mudgrubber
* For elf-likers, Treehugger
* For elf-likers, Grasseater
* For elf-likers, Leaflicker
* For elf-likers, Berryboy
* For gnome-likers, rootsucker
* For gnome-likers, mudboy
* For humans that breed with other races, sullier
* Nothing
* Shortlife
* Luster
* Dill (as in dilletante)
* Monkey
* Monkeyboy
* from underdweller, surface dweller
* Any made up word to represent another language
Lizardfolk:
* Lizzies
* Slit-eyes
* two-prongs
Note that some of these have slightly varying uses...
* To insult a race in general ("The pecks live over there.")
* To to insult a person by sole virtue of being a particular race ("You're just a peck.")
* To insult a particular person's effectiveness as a member of a race ("You're just a toolbreaker." to attack a dwarf's proficiency with tools - for comparison, much the same a human male may be insulted if his manhood was the subject of a joke)
* Even still, some of these can actually be used as terms of affection to a particular person with which the speaker has in fact a good relationship ("Let's go, Stumpy!")
Suggestion: Find the racial entry in the PHB or MM. Then find any single sentence relating to a racial ability, physical feature, habit/society, or physical environment. Now, take it to an extreme exageration (to insult the race in general from an outsider's point of view) or else take its reverse (to insult a person's effectiveness as a member of the race)