Games like Mushroom Age
Games like Mushroom Age include The Room, There Is No Game: Wrong Dimension, Morphopolis, That's not my Neighbor, and The Room 4: Old Sins. We matched them by the tags players give Mushroom Age on Steam (Adventure, Casual, Hidden Object, Puzzle, and Simulation): closest matches first, and among equally close ones the better-known games.

The Room
Shared: Puzzle · Adventure · Point & Click

There Is No Game: Wrong Dimension
Shared: Adventure · Puzzle · Point & Click

Morphopolis
Shared: Puzzle · Hidden Object · Casual

That's not my Neighbor
Shared: Adventure · Casual · Point & Click

The Room 4: Old Sins
Shared: Adventure · Puzzle · Point & Click

Boxes: Lost Fragments
Shared: Adventure · Puzzle · Casual

Hidden Through Time
Shared: Casual · Hidden Object · Puzzle

The Room Two
Shared: Puzzle · Hidden Object · Adventure

Hidden Folks
Shared: Casual · Hidden Object · Puzzle

Enigmatis: The Ghosts of Maple Creek
Shared: Adventure · Hidden Object · Casual

Storyteller
Shared: Puzzle · Adventure · Point & Click

Return to Monkey Island
Shared: Adventure · Point & Click · Puzzle

Grim Legends: The Forsaken Bride
Shared: Hidden Object · Casual · Adventure

Enigmatis 2: The Mists of Ravenwood
Shared: Adventure · Hidden Object · Casual

Frankenstein: Master of Death
Shared: Hidden Object · Casual · Adventure

The Room Three
Shared: Adventure · Puzzle · Point & Click

Grim Legends 2: Song of the Dark Swan
Shared: Casual · Adventure · Hidden Object

Lost and Found Co.
Shared: Hidden Object · Adventure · Point & Click

My Brother Rabbit
Shared: Adventure · Puzzle · Point & Click

Machinarium
Shared: Puzzle · Point & Click · Adventure

Enigmatis 3: The Shadow of Karkhala
Shared: Casual · Adventure · Hidden Object

Varenje
Shared: Adventure · Casual · Puzzle

The House of Da Vinci
Shared: Hidden Object · Puzzle · Adventure

The Silent Age
Shared: Adventure · Point & Click · Puzzle