Final Fantasy 5 - Laden with pitfalls inside. Quick sand outside. Gameplay is instantly recognizable, has a great job system to boot.
Secret of Evermore - You and your dog get separated, and have to help each other proceed to reunite, step on switches for each other to pass, find a weapon with the power to knock down certain walls, etc. Gameplay is like Secret of Mana, Seiken Densetsu, etc. Of note, this is Jeremy Soule's first work as a composer, and he had some help from his brother.
Shining the Holy Ark - South Temple is essentially a Pyramid, sarcophagi are treasure chests, most of which are rigged with a mummy-type enemy that sends your party flying back a square. May also contain hidden stairways to the next level. Walls block your way with a certain symbol that require a magic pickaxe. Some are destroyed, some are monsters in disguise.
You also find a stone that allows you to run through a spiral staircase, whereupon the entire dungeon needs to be traversed on the ceiling, so you can bypass certain obstructions on the ground.
Final room has a (somewhat simple) mathematics problem in order to break a seal on a Sacred Treasure.
Edit: Late addition, just remembered Persona 5. 4th dungeon is a gigantic pyramid that has you weave in and out of it, solving some puzzles along the way, avoiding boulders Indiana Jones-style, even fighting some Egyptian mythological creatures, which you can of course capture and use yourself. Like all dungeons in Persona, stealth is a mechanic for getting past, and surprising monsters.
Earthbound. You wander through a desert, and enter a subterranean pyramid through a Sphinx, by solving a puzzle. Much like Shining, treasure chests are all sarcophagi, enemies are mostly Egyptian-themed, but tongue-in-cheek. Basically Dragon Quest set in modern times in terms of gameplay.
Illusion of Gaia. SNES top-down ARPG. Historical fantasy version of Earth. You explore the actual Egyptian Pyramids. It's been so long since I played, but I do believe there is a puzzle involving a giant Condor to gain entrance inside. Other real life ancient wonders included are Angkor Wat, and The Great Wall of China. Tower of Babel is also in it I believe, as a small bonus.
Added a video clip of each game, sans earthbound (5 video limit). Alas, I couldn't find gameplay of Shining the Holy Ark without some clown talking over it. I know I hate hearing some dweeb talking over game footage, and figure most people here feel the same.