This is a personal selection of programs that I have found to be the most suitable and efficient for my tasks, that is correcting of scanned slides and negatives. If you do not agree, feel free to suggest a program in comments. If you are convincing enough, I might add it to the list.
Supported operating systems: Windows
From it’s site: IrfanView is a very fast, small, compact and innovative FREEWARE (for non-commercial use) graphic viewer for Windows. It is designed to be simple for beginners and powerful for professionals.
One of the first programs I always install on any Windows system I use. Although it started as a simple picture viewer in current version it is a powerful picture editor which includes all basic tools including batch processing and even more tools are available as plugins.
Supported operating systems: Linux, Windows, Mac OS X and others
From it’s site: GIMP is an acronym for GNU Image Manipulation Program. It is a freely distributed program for such tasks as photo retouching, image composition and image authoring. It has many capabilities. It can be used as a simple paint program, an expert quality photo retouching program, an online batch processing system, a mass production image renderer, an image format converter, etc. GIMP is expandable and extensible. It is designed to be augmented with plug-ins and extensions to do just about anything. The advanced scripting interface allows everything from the simplest task to the most complex image manipulation procedures to be easily scripted.
The unofficial free replacement for Photoshop with countless features and possibilities to correct pictures. There is nothing that can’t be done with this program (at least I have not found it yet). But you should take some time (and maybe even RTFM) to learn to use it.
Supported operating systems: Linux, Windows, Mac OS X
From it’s site: digiKam is an advanced digital photo management application. The people who inspired digiKam's design are the photographers like you who want to view, manage, edit, enhance, organize, tag, and share photographs.
Although the main focus of digiKam is tagging and organizing of pictures, it is also a very capable picture editor. I am only guessing, but it probably shares several graphics libraries with Gimp (which is a good thing). I like it’s picture editor, which allows me to work fast and effectively when correcting scanned slides.