Dropbox is a cloud storage service operated by Dropbox Inc. It offers 2GB of free storage space to backup photos, videos, files and important documents. Dropbox's Camera Upload feature allows you to automatically upload photos and videos to your Dropbox account from any device. It uploads photos and videos to the "Camera Uploads" folder in your Dropbox account. It gives name to them with the date and time they were taken. To view your photos and videos uploaded with Camera Upload, you can click "Photos" page in your Dropbox account online and by selecting the 'Photos' tab located at the bottom on the screen on mobile devices. Dropbox will not delete photos and videos from your mobile device after they are uploaded. You have to remove them manually. This "Camera Upload" feature is available for personal account users only.
You can install PicBackMan's Dropbox uploader for Mac from the website and start backing up photos and videos.