A project idea list is here: https://hackaday.io/project/5554-hackadayio-project-ideas-for-hackathon
Feel free to suggest some more project ideas!

Medical tricorder check out https://hackaday.io/project/4693-medical-tricorder
for inspiration!
Temperature sensor, bio sensor

Seismic detector
Vibration sensor, data collection via PC

Environmental monitor check out https://hackaday.io/project/4977-portable-environmental-monitor for inspiration
Temp, humidity, CO sensor

Solar light bulb check out https://hackaday.io/project/4760-nocturnal-solar-light-bulb for inspiration
Light sensor, solar panel (BYO solar panel)

Gas sensor helmet check out https://hackaday.io/project/4742-gas-sensor-for-emergency-workers for inspiration
CO sensor, LPG (natural gas) sensor

Smart home energy saver
Temp sensor, moisture sensor, time, camera talk to phone/ computer

Flood sensing check out http://njhurst.com/blog/01356576041 for inspiration
Teensy

Automated gardening/ farming
Moisture sensor, timer, Teensy or Arduino

Automated Pill Minder / Reminder Check out https://hackaday.io/project/4900-pill-minder-automatic-pill-dispenser for inspiration

Affordable CT (Computer Tomography) Scanner for the masses Check out https://hackaday.io/project/4740-100-ct-scanner-xray-desktop-3d-scanner for inspiration

Ultra Low-Cost Prosthetic Arm which can be built from everyday materials Check out https://hackaday.io/project/442-third-world-medical-equipment-arm and their own project page at http://thirdworldproblemsolving.weebly.com/index.html

Open Syringe Pump built for low cost targeting food, medical, and bio applications Check out https://hackaday.io/project/1838-open-syringe-pump

Combination Heart Monitor and Auto Dialer for emergency response...Check out https://hackaday.io/project/1026-lifeguard-a-e-autodialler

Portable Insulin / Bottle Cooler using a Peltier, Fan, Heatsinks - all very accessible...Check out https://hackaday.io/project/5161/logs

Wireless Medical Data Logger with Web Connectivity - Check out https://hackaday.io/project/1156-medicycle-urban-responder/log/9745-wireless-medical-data-transfer-to-the-web

Radiation detector
Geiger Muller tube, Arduino or other microprocessor