Here are my initial thoughts -

Depths - Submarine Depth Charges Horror, claustrophobia Ping for signs but don't wake giant monster Make way through underground caverns to rescue lost crew

- Falling into a city
    Cyberpunk / big city scape
    Base Jumping
    Descending through layers of the underworld

- mining
    Everyone will do this!
    How to make something original that isn't spelunky / Miner dig deep
    Mine for something odd?
    New mining mechanics?

- hacking

- emotional depths

- void / chasm
    Explore into dark world depths
    Darker the deeper you go
    light is currency/progress marker

- Fishing Game
    Simple deep fishing with screens
    Robot fish
    Matrix-style broken world

- Deep Space
    Explore procedural space
    Planets, bases and space stations

- Oil Rig Drilling
    Grid based drill guessing
    Clues with probes that cost
    Make money from drilling
    Environmental message/twist end

- Sending Probes
    Send probes into chasm to find things
    Depth is progress
    Upgrade probes
    Fun audio work here

- Forest Depths
    Trad fantasy combat game
    Get to the tower, dark forest
    Attack skele/goblins, get treasure, twist end
    The Fountain

- Depths of the machine
    Cyberpunk hacking
    Physical journey into the depths
    Akira style funicular elevator

Currently thinking of the last one with some kind of procedural way of creating rooms and chambers... however when searching ref I found a rock paper shotgun article about game devs being obsessed with large elevators like in Akira.. and now am less excited! :D