No one person invented the stills camera, these three answers give the names and first recorded events of the significant factors involved in their development.

1) In ancient times possibly back to the 4th century BC it was known that a darkened room with a small hole to the outside would project an image of the scene outside onto the opposite wall (although reversed and upside down). Aristotle used the system and called it Camera Obscura (the latin for Darkened Chamber). Artists used the system to help plan their work.

2) Thomas Wedgwood, made 'sun pictures' in 1800 by placing objects on leather that had been treated with slver nitrate. The effect of sunlight on silver had been noted in 1727 by Professor J. Schulze. Wedgwood's pictures faded quickly.

3) Nicéphore Niépce combined the camera obscura with photosensitive paper in 1816, but it was 10 years before he could make the image permanent. Eight years later in 1834 Henry Fox Talbot made negative images, which, by a process of contact printing was able to produce multiple copies.

The process went through incremental development from then on, significant dvelopments were colour photography invented by James Clerk-Maxwell in 1862. Kodak's first roll-film camera was produced in 1888 using a roll of paper 20 feet long it allowed 100 images to be captured. Kodak also produced the first digital camera in 1975. In 2004 Kodak stopped producing film cameras.

Sources:
http://inventors.about.com/od/pstartinventions/a/Photography.htm
http://photo.net/history/timeline
http://www.infoplease.com/ce6/sci/A0857142.html