IR remote for devices around the house: https://www.stavros.io/posts/how-turn-your-raspberry-pi-infr...

RF remote for more devices: https://www.stavros.io/posts/how-remote-control-rf-devices-r...

Home server for controlling various things around the house (farther down)

ESP8266:

A rotary mobile phone: https://www.stavros.io/series/irotary/

A button that orders food when pressed (Amazon-dash-like): https://www.stavros.io/posts/emergency-food-button/

Sensor board for sensing things in all the rooms of the house: https://www.stavros.io/posts/building-cheap-home-sensorcontr...

The above ties in with the Raspberry Pi farther up.

A LED strip controller: https://www.stavros.io/posts/wifi-enabled-rgb-led-strip-cont...

A toy bus with an OLED screen that shows which bus is passing by next (no post yet).

A self-driving RC car (no post yet).

A perfume sprayer that sprays perfume with an API (no post ever).

Arduino:

Nothing, the ESP8266 is better.

And these are just random ideas I got, you can do way more if you have a specific need for them.