Here's a couple of clips I've recorded a few months back.
(Note that links have been updated as a preventive measure against broken links.)
Game Title: Fairune 2Platform: 3DS
Area Number/Name: Green Fields, Green Fields Underground
Notes: Quicksand in the overworld can be bypassed with the Earth Ring, while similar traps underground cause instant death.
Game Title: HurricanesPlatform: Genesis
Area Number/Name: 3
Notes: Sinking in the sand here locks the player's mobility unless he/she is jumping out of it. Also, getting attacked while sinking will guarantee certain death.
Game Title: Hexyz ForcePlatform: PSP
Area Number/Name: Endless Sands
Notes: In this game, quicksand only serves to hinder movement or shift the player with its flow.
Game Title: Deltora QuestPlatform: DS
Area Number/Name: Chapter 2
Notes: As the story focuses on the book, there are two quicksand/swamp cutscenes to be encountered.
Game Title: An American Tail: Fievel Goes WestPlatform: SNES
Area Number/Name: Stage 4-1 and 4-3
Notes: Just some standard desert quicksand.
Game Title: Hard Corps: UprisingPlatform: PS3, Xbox 360
Area Number/Name: Desert
Notes: The provided video features clips of Krystal and Sayuri trudging all the way through the quicksand area.
Game Title: CrossCodePlatform: PC
Area Number/Name: Faj'ro Temple
Notes: Sinking into the sand here deals a fairly minimal amount of damage.
Game Title: YuquePlatform: PC
Area Number/Name: Sand World
Notes: The quicksand here leads to an underground facility, which contains an event that has a chance of triggering upon activating the monitor located near an unpowered machine.
Game Title: Metal Slug 7 (Metal Slug XX)Platform: DS, PSP
Area Number/Name: Mission 2
Notes: The quicksand pits here serve to leave the player vulnerable to enemy attacks, unless the player struggles out of it by mashing various buttons.
Game Title: Neopets (The Great Desert Race)Platform: Flash
Area Number/Name: N/A
Notes: Once a player character gets stuck in quicksand, he/she loses a turn and stays there, struggling or panicking, until said player's next turn is ready.
Game Title: Zelda II: The Adventure of LinkPlatform: NES
Area Number/Name: Swamp areas
Notes: This clip features a female Link from a ROM hack.
Game Title: Super MetroidPlatform: SNES
Area Number/Name: Maridia
Notes: My take on a clip I've shared long ago, where this rendition shows Samus slog and/or sink in the various quicksand pits in Maridia.
Game Title: SiNiSistarPlatform: PC
Area Number/Name: Test Forest
Notes: A game in development, which luckily contains a swamp section as part of the demo level. Once Rabiane sinks far enough, jumping will be disabled unless she wades into a more shallow area.
Game Title: Mace: The Dark AgePlatform: Arcade, Nintendo 64
Area Number/Name: Al' Rashid's Stage
Notes: Quicksand outside of the arena gradually damages the person in it. For this matter, the clip was recorded in Practice Mode to counteract said effect.
Game Title: Scooby-Doo! and the Spooky SwampPlatform: PC, PS2, Wii
Area Number/Name: The Swamp
Notes: Muddy areas reduce jumping distance and speed, and when a player steps into it, various reactions may sometimes be elicited.
Game Title: The Legend of Dark Witch - Episode 2Platform: 3DS, PC
Area Number/Name: Pasta Sandland
Notes: Quicksand in this game is non-lethal, since it only slows down the player.
Game Title: Miko to Akemi no Jungle AdventurePlatform: PC88
Area Number/Name: Level 2
Notes: Going north in a certain path leads to a bottomless swamp, which yields a still image where the two protagonists panic as they drown in the swamp, leading to a Game Over.
Game Title: Hands of TimePlatform: GBC
Area Number/Name: Level 8: Swamps
Notes: To cross the quicksand in this area, the life vest must be equipped.