This is a list of 2D games for standard definition home systems with foreground parallax, which can be obtained by using an extra foreground layer (hardware support) or an additional pseudo-layer (software implementation).

The foreground parallax can be used to improve the depth sensation in side scrolling games as well as to provide in game fullscreen graphical effects without pausing the gameplay. Some other uses are also possible but less common. 

Special thanks to the Sega-16 members goldenband, sheath, NeoVamp, Lync, Zebbe, Bottino, midnightrider, cowboyscowboys, Black_Tiger, TmEE, Foxysen, The Coop, Silence The Fallen, Guntz, LongAnimals, j_factor and Christuserloeser  for contributing to the Mega Drive/Genesis list. 
See the discussion here. 

Sega Mega Drive/Genesis (1988 hardware)
Aero the Acro-Bat 2 (1994)
Demo: youtu.be/xaZsgyxJzyE*** | youtu.be/aT7sRSCPogg?t=14m5s***
Alien Soldier (1995)
Demo: youtu.be/d_C4poYiz0k | youtu.be/3DezQgPPD3I
Alisia Dragoon (1992)
Demo: youtu.be/wdiSnneMrLQ?t=13m48s
Altered Beast (1988)
Demo: youtu.be/4LDI_XRwezA?t=1m12s
Arrow Flash (1990)
Demo: youtu.be/eUp3Xpt7eB8?t=1m6s | youtu.be/eUp3Xpt7eB8?t=3m28s
Art of Fighting (1993)
Demo: youtu.be/WB7aeGOtDYo?t=9m26s
Asterix and the Great Rescue (1993)
Demo: youtu.be/h1hOJ0tLNo4?t=2m34s
Asterix and the Power of the Gods (1995)
Demo: youtu.be/WowqaANEZLo?t=3m40s | youtu.be/WowqaANEZLo?t=50m20s
Batman (1990)
Demo: youtu.be/LN3edTR7Xb4?t=11s
Batman Forever (1995)
Demo: youtu.be/NiAwnb-2q0o?t=1m29s
Batman Returns (1992)
Demo: youtu.be/FQOk-p_k0_c?t=5m2s***
Battle Mania: Daiginjou (1993)
Demo: youtu.be/rZ5cexuBW2Q?t=31m37s
Battle Squadron (1990)
Demo: youtu.be/XnJmse4h8TY?t=4m26s
Bishoujo Senshi Sailor Moon (1994)
Demo: youtu.be/F5uV_nJ3SoI?t=7m37s | youtu.be/fxxT5YAdLYI?t=56s | youtu.be/fxxT5YAdLYI?t=5m37s
Blades of Vengeance (1993)
Demo: youtu.be/wN6X3BbPYRY?t=2m30s
Bram Stoker's Dracula (1993)
Demo: youtu.be/sUciMmBV1cY?t=7m
Bubba 'n' Stix (1993)
Demo: youtu.be/ojuuzSd6ziE?t=33s
Cheese Cat-Astrophe Starring Speedy Gonzales (1995)
Demo: youtu.be/AAcb9KJl5c4?t=1m59s
Chelnov (1992)
Demo: youtu.be/sw8P5AEDln0?t=7m33s
Chester Cheetah: Too Cool To Fool (1992)
Demo: youtu.be/lktMpRHItuc?t=2m10s
Chester Cheetah: Wild Wild Quest (1993)
Demo: youtu.be/ifZiILfxBk0?t=11s
Chuck Rock II: Son of Chuck (1993)
Demo: youtu.be/BIjqmQRmbwo?t=11m12s
Contra: Hard Corps (1994)
Demo: youtu.be/_mV5PhYxaaU?t=4m33s | youtu.be/smDF1-p743g?t=9m44s | youtu.be/smDF1-p743g?t=11m27s
Crystal's Pony Tale (1994)
Demo: youtu.be/dycnfHXZ8Rw?t=2m27s
Desert Demolition Starring Road Runner and Wile E. Coyote (1995)
Demo: youtu.be/sbf1rSxp500?t=7m8s
Disney's Aladdin (1993)
Demo: youtu.be/9VR8acEbLV0?t=19m51s | youtu.be/9VR8acEbLV0?t=35m45s
Disney's Beauty and the Beast: Belle's Quest (1993)
Demo: youtu.be/MfEgvJF_GaE?t=4m18s | youtu.be/MfEgvJF_GaE?t=4m29s
Disney's Beauty and the Beast: Roar of the Beast (1993)
Demo: youtu.be/wyG7xxXrQt8?t=1m33s | youtu.be/MfEgvJF_GaE?t=15m7s
Disney's Bonkers (1994)
Demo: youtu.be/NXkp1ImxiIY?t=1m25s
Disney's Pinocchio (1996)
Demo: youtu.be/Gn5fOJqTscI?t=15m3s | youtu.be/f5fXmfmKyBI?t=4s***
Disney's Pocahontas (1996)
Demo: youtu.be/zj4gOd4kffg?t=31m27s***
Disney's The Lion King (1994)
Demo: youtu.be/Zp0FploW1Os?t=50m51s
Disney's Toy Story (1996)
Demo: youtu.be/p5L-YtrQg5k?t=13m53s
DJ Boy (1990)
Demo: youtu.be/kAhHjImK-FY?t=37s | youtu.be/my99_m2f3sU?t=6m23s
Doom Troopers (1995)
Demo: youtu.be/GkhOWn2SVQ4?t=7m5s
Dragon: The Bruce Lee Story (1994)
Demo: youtu.be/0isP6gr9S3Q?t=5m34s | youtu.be/0isP6gr9S3Q?t=6m8s
Dragon's Lair (1993 - Previously Unreleased)
Demo: youtu.be/S9xWbIhC-0Q?t=21s***
Dynamite Headdy (1994)
Demo: youtu.be/LHTWLcaJXcE?t=7m15s
Earnest Evans (1992)
Demo: youtu.be/lxxPbyAb0Ac?t=12m10s
Earthworm Jim (1994)
Demo: youtu.be/rmhJAFsQVhM?t=1m38s
Earthworm Jim 2 (1995)
Demo: youtu.be/EretZPOQHM0?t=1m59s
Eliminate Down (1993)
Demo: youtu.be/xT38VjKxOZI?t=1m33s
ESWAT: Cyber Police (1990)
Demo: youtu.be/VaK7ofbGIcw?t=6m10s***
Eternal Champions (1993)
Demo: youtu.be/6g9cab6qibc?t=7m46s | youtu.be/w9RoU32zO68?t=37s | youtu.be/BbZhFxFgAr4?t=35s
Ex-Mutants (1992)
Demo: youtu.be/3TeddbM2xgc?t=29s | youtu.be/b6kaXN5Cwmk?t=27s | youtu.be/f8yOKgCv7F8?t=25s
Exo-Squad (1995)
Demo: youtu.be/INnOE0Tbsug?t=2m50s*** | youtu.be/KgQjtx8tkI8?t=38s***
Fantasia (1991)
Demo: youtu.be/Mx04FvJUPdA?t=54s
Fatal Fury (1993)
Demo: youtu.be/o5GovV0c3pk?t=1m54s***
Fatal Fury 2 (1994)
Demo: youtu.be/FY2z477usHw?t=2m51s
Flink (1994)
Demo: youtu.be/lxa3LtzRfDg?t=1m30s
Gaiares (1990)
Demo: youtu.be/fonV4oT4haw?t=5m44s
Garfield: Caught in the Act (1995)
Demo: youtu.be/EO4vwfg6Ie0?t=9m10s | youtu.be/jvL5J7G_yJI?t=13m46s
Gargoyles (1995)
Demo: youtu.be/wzW0aP771Kw?t=4m7s***
Golden Axe (1989)
Demo: youtu.be/Yr8-woRCEiM?t=4m46s | youtu.be/Yr8-woRCEiM?t=10m25s
Golden Axe III (1993)
Demo: youtu.be/SODJu5CvlhY?t=9m33s
Gunstar Heroes (1993)
Demo: youtu.be/sk7pt--94ko?t=15m | youtu.be/sk7pt--94ko?t=47m4s
Gynoug (1991)
Demo: youtu.be/MWBMUNKUyzo?t=10m2s
Heavy Nova (1992)
Demo: youtu.be/1VlfPZ-LUA4?t=10m38s
Magical * Taruruuto-kun (1992) 
Demo: youtu.be/ACJDs805nKc?t=2m11s
Maou Renjishi (1991)
Demo: youtu.be/CgAGrZLzTbA?t=6m5s
Marko's Magic Football (1994)
Demo: youtu.be/YJnkIee-7ag?t=6m46s
Marsupilami (1995)
Demo: youtu.be/U-ugr85SWDQ?t=1m39s
Mazin Saga Mutant Fighter (1993)
Demo: youtu.be/dYdnP10TIj8?t=3m12s
McDonald's Treasure Land Adventure (1993)
Demo: youtu.be/hiozOQWed6o?t=1m48s
Mega Turrican (1994)
Demo: youtu.be/Tp5XlH90Sgc?t=38m7s
Michael Jackson's Moonwalker (1990)
Demo: youtu.be/zk1C0AhshtU?t=7m51s
Mick & Mack as the Global Gladiators (1992)
Demo: youtu.be/TwT9UlOrYiI?t=1m57s
Mickey Mania (1994)
Demo: youtu.be/inCunWkTllA?t=1m20s
Mighty Morphin Power Rangers (1994)
Demo: youtu.be/fPQ4eiSJ4sI?t=1m55s
Mighty Morphin Power Rangers: The Movie (1995)
Demo: youtu.be/170Lp542McU?t=2m34s | youtu.be/LPY1B8bN7lI?t=8m32s
Monster World IV (1994)
Demo: youtu.be/CX5_pBnADfY?t=4m45s***
Mortal Kombat 3 (1995)
Demo: youtu.be/IIc0zPyeXFI?t=13m13s
Mr. Nutz (1994)
Demo: youtu.be/_WuHK1iA7LsLs?t=1h16m15s***
Mr. Nutz 2 (1994 - Previously Unreleased)
Demo: youtu.be/dR8bL9dMuHI?t=50m31s***
Mystic Defender (1989)
Demo: youtu.be/cujc_0c7MYs?t=2m7s
Outlander (1992)
Demo: youtu.be/OHPB_IxEDSA?t=5m3s
Phantasy Star II (1989)
Demo: youtu.be/eoUL9AdKrEY?t=7m55s | youtu.be/eoUL9AdKrEY?t=14m48s
Pink Goes to Hollywood (1993)
Demo: youtu.be/M5DkoZ8kOv8?t=9s
Psycho Pinball (1994)
Demo: youtu.be/d630TiyrH9U?t=1m36s
Puggsy (1993)
Demo: youtu.be/ztkNek9MNgw?t=6m33s***
Pulseman (1994)
Demo: youtu.be/qiZCl1iDhLw?t=6m33s | youtu.be/S9-rb0Sh5HU?t=1m27s
Ranger X (1993)
Demo: youtu.be/Z8A2Yyg3eAs?t=1m54s | youtu.be/JHmRyankggk
Red Zone (1994)
Demo: youtu.be/NQxU2CIVb3c?t=7m57s
Ristar (1995)
Demo: youtu.be/vM0jSdPxe3o?t=10m20s
Rolling Thunder 3 (1993)
Demo: youtu.be/ufsqktw34DI?t=6m29s
Second Samurai (1994)
Demo: youtu.be/uWAMPtEcBFU?t=40m9s***
Shadow of the Beast (1991)
Demo: youtu.be/m2peJvG0MUc?t=6s
Shaq Fu (1994)
Demo: youtu.be/YmpDh2sTc2s?t=2m
Sol-Deace (1992)
Demo: youtu.be/BhuVh-nalCs?t=16s
Soleil (1994)
Demo: youtu.be/4NIXM0sFATo?t=2m57s | youtu.be/D9DNIpSVjLc?t=10m15s | youtu.be/Wmvp59p86Po?t=4m48s
Sonic The Hedgehog (1991)
Demo: youtu.be/x7PGguaSD5k
Sonic The Hedgehog 2 (1992)
Demo: youtu.be/IRQ1QTA1YTc
Sonic The Hedgehog 3 (1993)
Demo: youtu.be/gnokWaBb16s?t=1m30s
Splatterhouse Part 2 (1992)
Demo: youtu.be/H2rv4cf87lg?t=13m25s | youtu.be/H2rv4cf87lg?t=19m34s | youtu.be/H2rv4cf87lg?t=31m26s
Street Fighter II' Plus: Champion Edition (1993)
Demo: youtu.be/S8KsOFYB75M?t=5m20s
Streets of Rage (1991)
Demo: youtu.be/H_Iu9mJbHWE?t=40m16s
Streets of Rage 2 (1992)
Demo: youtu.be/rxg1ofbrISU?t=5s
Streets of Rage 3 (1994)
Demo: youtu.be/17WJhdscUhQ?t=3m6s
Sunset Riders (1992)
Demo: youtu.be/l_nACIsPNXM?t=1m36s
Super Airwolf (1991)
Demo: youtu.be/-3DM4Ob68IA?t=2m59s
Super Smash T.V. (1992)
Demo: youtu.be/qoh_tREhoLI?t=1m25s
Super Street Fighter II: The New Challengers (1994)
Demo: youtu.be/RermPMEp8MM?t=2m14s
Sword of Sodan (1990)
Demo: youtu.be/_ABEaPRCydI?t=1m59s | youtu.be/_ABEaPRCydI?t=4m53s | youtu.be/_ABEaPRCydI?t=6m40s
Taz in Escape from Mars (1994)
Demo: youtu.be/MJhaVvKIx4k?t=26m21s*** | youtu.be/MJhaVvKIx4k?t=39m23s***
Teenage Mutant Ninja Turtles: Return of the Shredder (1992)
Demo: youtu.be/Ditki1yqF3Q?t=7s
The Adventures of Batman & Robin (1995)
Demo: youtube.com/watch?v=C3KO3bBPjg0
The Great Circus Mystery (1994)
Demo: youtu.be/l5MWaxbzIuw?t=8s*** | youtu.be/fs7Kntk78Nw?t=1m30s***
The Pirates of Dark Water (1994)
Demo: youtu.be/SLxqWFw2tTc?t=1h3m23s***
The Ren & Stimpy Show Presents: Stimpy's Invention (1993)
Demo: youtu.be/TJ8q_ouyZxo?t=2m15s
The Super Shinobi (1989)
Demo: youtu.be/77-jO0NVahk?t=14s
The Super Shinobi II (1993)
Demo: youtu.be/STdb3YDwuEg?t=13s
Thunder Force IV (1992)
Demo: youtu.be/UMB-OAodJ4w?t=1m56s
Time Dominator 1st (1994)
Demo: youtu.be/SRl8UNzmGpk?t=7m10s***
Time Trax (1994 - Previously Unreleased)
Demo: youtu.be/hHS-JvSPfgk?t=3m28s*** | youtu.be/hHS-JvSPfgk?t=7m40s***
ToeJam & Earl in Panic on Funkotron (1993)
Demo: youtu.be/HshXSNqM9cI?t=11m30s | youtu.be/Ya_OPSPRKDI?t=14m32s
Tom Mason's Dinosaurs for Hire (1993)
Demo: youtu.be/j-MtPtZwgF8?t=2m20s
Toxic Crusaders (1992)
Demo: youtu.be/99w2RdyoiT4?t=1m29s
Vampire Killer (1994)
Demo: youtu.be/YVP1I7l9PJ0?t=32s | youtu.be/YVP1I7l9PJ0?t=18m| youtu.be/YVP1I7l9PJ0?t=28m25s
Vectorman (1995)
Demo: youtu.be/IORZ49e-b1U?t=19m5s | youtu.be/IORZ49e-b1U?t=23m21s | youtu.be/IORZ49e-b1U?t=31m27s
Vectorman 2 (1996)
Demo: youtu.be/NsC__n59jmI?t=14m6s
X-Men 2: Clone Wars (1995)
Demo: youtu.be/Kg57aoaG7Sc | youtu.be/VnBTzkVrVJ0?t=19m46s
Whip Rush (1990)
Demo: youtu.be/Oh2yym2VRuk?t=1m41s
Wonder Boy V: Monster World III (1991)
Demo: youtu.be/KEtumiBjpqQ?t=8m41s
World of Illusion Starring Mickey Mouse & Donald Duck (1992)
Demo: youtu.be/z14tilKYHL8?t=2m15s
Yogi Bear's Cartoon Capers (1994)
Demo: youtu.be/Z4r5SXXk-VU?t=40m54s***
Yuu Yuu Hakusho: Makyo Toitsusen (1994)
Demo: youtu.be/MnCG84LmgMQ?t=1m11s
Zero the Kamikaze Squirrel (1994)
Demo: youtu.be/ZVTkFVcFHfg?t=37m27s*** | youtu.be/ZVTkFVcFHfg?t=46m34s***

Total: 127 games

Gameplay demos are from real hardware unless stated otherwise.
***Only emulated gameplay videos are available for this part of the game.