Say what you will about mobile phones, their cameras have improved faster than anyone could have predicted with the blend of hardware and software upgrades, as well as a lot of innovation. In this video, watch some creative shots that can be taken with just a phone.
I first started taking my phone seriously as a camera two years ago when I didn't want to take my long prime lens off of a camera I was reviewing. I decided to see what my phone could do as a replacement for a wide-angle setup. I was thoroughly impressed. That's not to say it's always right when you need a wide-angle lens, but if you don't need a narrow depth of field and the file is unlikely to go under heavy scrutiny, post-production, or cropping, it can do a job.
The benefits of a camera phone are obvious. You more or less always have one on your person, they fit in your pocket, and they are inconspicuous. The downsides are that you can't change the lenses, you can't get optical narrow depth of field, and the files aren't overly malleable. All of these downsides can be worked around in one way or another. What I found to be the most important tip for phone photography is that composition is essential if you want a good shot. This is true of most types of photography, but becomes even more important when you're using a camera that isn't dedicated.