First up, the camera effects. Bringing up this little screen below lets you choose from a variety of effects
The Solarize setting is one of my favourites and can be stunning at night:
And distortion can create some pretty quirky effects with the right composition (or just a friend's face, your choice!).
For anyone doubting that mobile photography is a legitimate method of producing art, the HTC One provides a pretty good (8mp) argument. If you're still not sure, here's a picture of a book I saw at the Tate Modern at the weekend, and a link to the book on amazon. It's a bit out of date though, as One X doesn't seem to feature...