Thanks to Dropbox's code wizardry (clever caching or something else), Carousel breezes through your entire photo collection without waiting for thumbnails to load. It also lets you share, like, and comment photos in your personal gallery, in addition to automatically organizing them by time, date, location, and other properties.
Since we can't have a Dropbox app without cloud storage functionality, Carousel will automatically back up your photos to your Dropbox account. You can run it alongside iCloud or other backup services, of course.
Although Carousel is, (not very) deep down, another way for Dropbox to get you to buy more gigabytes of their cloud storage, it seems to be a quality app. For example, it has a smile detection algorithm built into it, which scans photos containing faces for the best smile, and chooses the best thumbnail for each collection. Unfortunately, not everything about it is as seamless. Not unlike other non-ubiquitous communication apps, if you try to share a photo with a contact that doesn't have Carousel installed, all said contact will be able to see is a small thumbnail bundled with a link to download the app.
Carousel is available from the links below. You might find it interesting that the app looks almost the same on both Android and iOS. Can you guess which screenshot's which?