I used a raspberry pi 2. I was tracking the movement of a plant in my apartment http://imgur.com/a/hoEwO
I used a simple cron job to capture photos in the waking hours of the day and upload to a cloud drive. Was definitely a fun project. I was hoping to eventually expand the project to include image detection so I can keep track of the various animals roaming my apartment. Also, create a mobile app that would allow me to snap pictures or videos remotely, but haven't gotten around to it yet.
I used it to capture a timelapse of few days:
And yes, this is one of my favorite Pi projects too; it's one of the few where I can show my wife the results and she doesn't just roll her eyes at me.
Alternatively, you could use something like an Arduino, and connect it in some way to an independent camera. Since it doesn't need to process the picture, you don't need a powerful processor or MBs of RAM.
The AUKEY supply I'm using goes for about 6 days, continuous.
You can also have two packs and judiciously swap them out every week or so. That's my plan for a video I want to record later this year.
https://github.com/bschwind/timelapse-zero
I even have the same carbon fiber case:
http://i.imgur.com/PF5kri7.png
Though I did this before the Zero W came out so I had to have that ugly USB hub and WiFi adapter there. Something is being built across the street from me which is what prompted me to set this up.