This list will be periodically updated as I remember songs/artists. This is, by no means, a comprehensive list of South Korean hip-hop/rap artists, nor will it probably ever be, as the underground Korean rap scene is massive.
Rap/Hip-Hop Groups (these fall outside of mainstream K-Pop)
*CMYK (aka Sunday 2PM) - "Too Crazy" -- "Since Byeonsatto" (this is my favorite rap group)
*Dynamic Duo - "Baaam" feat. Muzie (of UV) -- "Hot Wings" feat. Hyorin (of Sistar)
*Epik High - "One" feat. JiSun -- "Map the Soul"
*Geeks - "Hangover" -- "Fly"
*M.I.B - "G.D.M" -- "Chisa Bounce"
*MFBTY (made up of Tiger JK, Yoon MiRae, and Bizzy) - "Sweet Dream" -- "Angel"
*Mighty Mouth - "Tok Tok" feat. Soya -- "I Love You" feat. Yeh
*Miss $ - "You Were Not the"... feat. Verbal Jint -- "Good Night"
*Phantom - "Hole in Your Face" -- "New Era" feat. Navi
*Supreme Team - "Dang Dang Dang" -- "I Just Need You" feat. Gaeko (of Dynamic Duo)
*Troy - "Why Are We?" -- "Green Light"
*Untouchable - "You You" feat. Oh JinSeok -- "Make a Fuss" feat. Vasco
Rap/Hip Hop Influenced K-Pop Groups (mainstream pop groups)
*1TYM - "Hot" (1TYM was one of the first hip-hop/pop groups on the scene)
*Airplane - "So Pretty" -- "Back to the Future"
*B.A.P - "One Shot" -- "Warrior" (this is my favorite pop group)
*Big Byung (made up of Jackson of Got7, N and Hyuk of VIXX, and SungJae of BtoB) - "Stress Come On"
*Bigstar - "Run and Run" -- "Be Brave"
*Block B - "Very Good" -- "Jackpot"
*BTS - "Hormone War" -- "No More Dream"
*Evol (girl group) - "Get Up" -- "Magnet"
*MadTown - "YOLO" -- "What's Your Number?"
*Sonamoo (girl group) - "Deja Vu"
*Speed - "Look At Me Now" -- "Don't Tease Me", "Why I'm Not"
*TOPPDOGG - "Arario" -- "Open the Door"
*WonderBoyz - "Tarzan" -- "Open the Door"
Solo/Underground Artists (these are also outside of the mainstream)
*Bizniz - "I Didn't Know" feat. Jang HyeJin -- "Get it Wet" feat. Shorry J (of Mighty Mouth)
*Crucial Star - "Paris" -- "Shops Selling Dreams" feat. Bob James, Mayson the Soul
*Deepflow - "I'm the Craziest Motherfucker Around Here" feat. G9, New Champ -- "Skillist" feat. San-E, Basick
*Dok2 - "They Love Who?" -- "ChiGiChaGaChoGoCho"
*Drunken Tiger (Tiger JK) - "Isolated Ones, Left Foot Forward!" -- "The Cure"
*Etikid - "Head Up" -- "Toast" feat. Deuce Fantastick
*Fame-J - "Not Human" feat. Jeebag (of CMYK) -- "Island"
*Garion - "Old Story" feat. Seven -- "Tree With Deep Roots"
*Huckleberry P - "Man in Black" -- "Rap Badr Hari"
*i11evn - "Factory Boy" -- "Broken Radio"
*Illinit - "What Do You Learn in School" -- "Lost" feat. Hwayobi
*Jolly V - "Bad Bitches" -- "Yes! Yes! Yo!" feat. JooAn
*Lil Cham - "Bad" feat. i11evn -- "Dangerous" feat. Verbal Jint, JeonGun
*Mad Clown - "Without You" -- "Stalker" feat. Crucial Star
*Masta Wu - "Come Here" feat. Bobby (of iKON), Dok2 -- "Don't Stop"
*MC Mong - "Sick Enough to Die" feat. Mellow -- "Circus"
*MC Sniper - "Go to Sleep" feat. BK -- "Coke Bottle" feat. Bumkey (of Troy)
*Okasian - "Pshh" -- "Lalala" feat. Beenzino
*Outsider - "Alone" -- "Hero" feat. LMNOP (Outsider is widely accepted to be one of the fastest rappers in the world)
*P-Type - "Turning Point" -- "Die Hard" feat. ALi, MC Meta
*The Quiett - "Livin' the Dream" -- "Tomorrow"
*Roydo - "Celebration" feat. Taewoon (of Speed), Mino (of Winner), and Scotch Vip -- "Look Around" feat. SIMS (of M.I.B)
*San-E - "Break Up Dinner" feat. Sanchez (of Phantom) -- "Black Suit" (Rphabet is a producer, San-E raps in this track)
*Scotch Vip - "The Finale" feat. Jay Moon, Mino (of Winner), Yammo, VeexKilla, Hanhae (of Phantom), Kyung and Zico (both of Block B), Qwala -- "No Time Out" feat. Mino (of Winner), Jolly V
*Swings - "Bulldozer" -- "Fallin'" feat. Jay Park
*Tymee (aka E.via) - "From Your Bitch" -- "Insanity Love" feat. LeeSu (of MC the Max)
*Verbal Jint - "Rare Breed" feat. YDG -- "If It Ain't Love" feat. Ailee
Misc./Collaborations/Single Songs (some mainstream artists, some underground)
*5Zic (of M.I.B) - "Beautiful Day"
*Bang YongGuk (of B.A.P) feat. YoSoeb (of B2ST) - "I Remember" (One of my all time favorite songs)
*CL (of 2NE1) - "The Baddest Female"
*Deffinite feat. Jeebag (both of CMYK) - "Breakdown"
*Epik High feat. Beenzino, Verbal Jint, B.I. and Bobby (both of iKON), Mino (of Winner) - "Born Hater"
*Factory Boi (record label) - "Why So Serious"
*G-Dragon (of Big Bang) - "A Boy"
*G-Dragon (of Big Bang) feat. Missy Elliott - "Nilliria"
*G-Dragon (of Big Bang) feat. Tablo (of Epik Hight), Dok2 - "Light It Up"
*G-Dragon & T.O.P (both of Big Bang) - "High High"
*G-Dragon & Taeyang (both of Big Bang) - "Good Boy"
*Gaeko (of Dynamic Duo) - "Rhythm is Life"
*i11evn feat. DJ Wreckx, Zico (of Block B) - "Mic Ceremony"
*Illionaire Records (record label) - "YGGR"
*Jay Park feat. Simon D (of Supreme Team), Gray - "Metronome"
*Jeebag (of CMYK) - "No Mosaic"
*Jucy (of Evol) feat. Deepflow - "Jucy Fresh"
*Kanto (of Troy) feat. Kim Sungkyu (of Infinite) - "What You Want"
*Kyung (of Block B) and Mino (of Winner) - "Be Quiet" (Samples Justin Timberlake's "Cry Me a River")
*LE (of EXID), JunHyung (of B2ST), and Feeldog (of Bigstar) - "You Got Some Nerve"
*Mino (of Winner) - "I'm Him"
*Outsider, KEIKEI, Maslo, CSP, Kirbytrap, L.E.O, illinit, Huckleberry P, JJK, Diz'one, Deffinite & Jebag (of Sunday 2pm), LMNOP, Marco, FANA, KyFish, and TakTak 36 - "Speed Racer"
*Rap Monster, Jin, and Suga (all of BTS) - "School of Tears" (Samples Kendrick Lamar's "Swimming Pools")
*Skrillex feat. G-Dragon, CL, Diplo - "Dirty Vibe"
*SIMS (of M.I.B) - "Hands Up"
*T.O.P (of Big Bang) - "Doom Dada"
*Tablo (of Epik High) feat. Taeyang (of Big Bang) - "Tomorrow"
*TaeWoon (of Speed) - "Focus"
*V.Hawk (Formerly Master One of WonderBoyz) - "Pupil"
* Yano feat. Sangdo (both of TOPPDOGG) - "Happy" (Samples Pharrell Williams' "Happy")
*Zico (of Block B) - "No Limit"