The following applications and plugins all utilise the Flickr API. You can read more about the API here.
Web Applications
Flickr Chia Pet
a collaborative defacement software toy that grows green hair on photographs.
Submit your photos of hairless cats, bald husbands, humvees and other things in need of a little chia goodness to the Naked Chia Pet group.
Flash-based Kaleidoscope
A Flash-based Kaleidoscope using recent thumbnails from the Squared Circle group.
Flickr Graph
"Flickr Graph is an application that explores the social relationships inside flickr.com. It makes use of the classic attraction-repulsion algorithm for graphs. Start exploring your contacts by entering your flickr username or the email address you used to register there."
'Color Fields' Color Picker
This widget finds photos from the group pool that match a color of your choice. Also available for Flickr Central and Squared Circle.
Mappr (US only)
A web-based application which uses tag information to place thumbnails of photostream images on a map of the US.
Flickr RSS Reader
"Flickr RSS Reader is an application built in Macromedia Flash MX 2004 Professional. This application reads RSS Feeds from www.flickr.com. It can run on your computers' hard drive or on your website."
FlickrReplacr
"You can highlight any word on any web page, click the flickReplacr bookmarklet, and the word gets swapped out with a random image from flickr that was tagged with that word."
Plugins/extensions
Flickrfox (Firefox Extension)
"Flickrfox is an extension for Firefox (version 1.0) that lets you browse your Flickr photostreams in a sidebar. You can find development updates on my blog."
Flickr Gallery (WordPress)
A WordPress plugin that lets you integrate your Flickr photos with your Word Press blog (Complete with support for notes and sets!).
Flickit (WordPress)
Flickit is a WordPress plugin that'll help you post photos to your weblog easily. Flickit gives you the ability to search through your own Flickr Photos and all public photos based on tags. Run a search for your own username, and pull up a list of your contacts and see their images, you can insert these images into your blog post.
Currently it only works with WordPress, but releases for Movable Type and Textpattern are coming soon.
Flickr Photosets (Movable Type)
Flickr Photosets is a Movable Type plugin that'll help you list your Flickr photo sets on your Movable Type blog.
Kubrickr (WordPress)
Since the release of WordPress 1.5 with Kubrick as the default theme, an awful lot of weblogs look the same. Owen Winkler has built an application that lets you use images from Flickr to replace that big blue blob header in your WordPress 1.5 Default theme.
Flickrpress (WordPress)
This script will get all of the photos uploaded to flickr by a specific user in the last 24 hours. It will then post the thumbnails to a Wordpress blog.
Mac applications
1001
"1001 is a desktop client to be used in conjunction with Flickr, the online photo-sharing website. 1001 not only uploads photos to your Flickr account, it notifies you anytime new photos from either your contacts, everyone, or your favorite tags are uploaded. 1001 allows you to step into the stream of photos passing through Flickr and to quickly see what's new at the moment. Just run the app in the background and if triggered, 1001 pops up a small unobtrusive window to notify you of new photos.
1001 comes with a Flickr screensaver that will incrementally display the latest image from Flickr. You must have run 1001 at least once to get the Flickr screensaver going. "
Flickr Export
FlickrExport is a plugin for iPhoto 4 which provides a direct export interface to Flickr.com
PictureSync
Upload your images, with metadata, from iPhoto, iView MediaPro, and files with or without IPTC fields. Includes resizing and metadata options.
Windows Applications
Flickr Screensaver v3
Turns your computer into a slideshow of Flickr photos when you're not using it. You can configure it to display photos from a particular person, from a particular group, photos with a certain tag, and more.
Kaleidoscope Screensaver
A kaleidoscopic screensaver which uses images from the squared circle Flickr group
Linux Applications
FlickrUploadr
"FlickrUploadr is a tool to upload your pictures to Flickr. There are some official tools for this task, but they aren't available on Linux, so I wrote my own."
jUploadr
A flickr uploader for Linux:
jUploadr is a cross-platform uploader for both linux and windows. It supports uploading photos to flickr, changing privacy settings, and editing all other properties of a photo (description, title, tags). To help with bulk uploading, you can edit several photos at once. see jUploadr's webpage (http://juploadr.sourceforge.net) for updates.