I don't have a camera on my cell phone (and I'll do everything in my power to keep it that way...but that's another story)...so for me, my 'crappy' camera is an ultra-compact P&S that I bring with me absolutely everywhere when my main camera isn't with me. It allows me to take spontaneous, strange, and spur-of-the-moment shots, as well as those 'don't want to miss' moments.
I take two different kinds of photos with my ultra-compacts - one, is when I take it along as my night camera or event camera when I don't want the big one along - but in those cases, I'm taking the time to compose, meter, and set up a shot - so I don't think those count in the 'crappy camera' thread, since I used whatever skill I have to take them to the best of the camera's ability.
The other type of photo is the spontaneous snap - sometimes just lifting the camera and firing the shutter, sometimes shooting blind over my head or backwards, sometimes a strange angle where I can't really see the shot being lined up because I'm holding it down by my ankles. Those are the shots I'm just having fun with, or saw something that I figured I'd make a halfass effort to shoot while driving or walking. Sometimes, you get some cool shots that way, and sometimes you don't. I delete them if they stink, but every once in a while get something I like.
Here's a shot taken while driving home from work...the sky in the rear view mirror looked brilliant, so I opened my sunroof and stuck my T100 out facing backwards and snapped a blind shot at 50mph:
I never even saw the sunset with my own eyes - only what I saw later looking at the camera!
Here's another nice sky I shot in my side-view mirror sitting at a stoplight:
Here's a commute TO work, just after a quick rainshower and the sun popped out with a nice rainbow - taken through the windshield while driving:
Here's boredom on a rainy day...I had a waterproof case for my older ultracompact, so I decided to walk out on my patio during an all-day rainstorm, and stick it on the ground in a puddle to shoot the yard from an ant's point of view - another blind shot: