This list of useful programs will be edited on an ongoing basis as more suggested programs are brought to our attention.
Image OrganizationCompuPic Pro - I've been using this for years. Good for basic (and advanced) browsing and organization. And basic editing, too. Has some helpful functions like auto-crop, batch conversion and renaming, keywords and categories for sorting, screensavers, slideshows, picture indexes, changing the time and date of files, looking inside .ZIPs easily, and finding out what type a file really is. It can do a lot (I'm still finding things that it can do), all you need to do is click around.
Font MakingBitmap Font Writer - Incredibly useful if you want to label your maps, but only want to do so with the game's own font. Or any custom font you may want to create, really.
Image CheckingRevned's Tile Slicer/Splicer - If you make your maps as nice rectangles with dimensions that are multiples of 16, these programs will slice them up into all its unique 16 x 16 tiles. You can then replace tiles that aren't the same (but should be) with ones that are and then splice them back together for a perfect map.
Revned's Tile Slicer (latest version, 1.1) - added May 2008, Splicer to come.
Image CompressionPNGGauntlet - I've been using this on every .PNG submitted to me, and nearly always am able to shrink them down. Depending on what you use to edit your .PNGs, this could shrink the filesize by quite a lot without affecting the image. Use this after you have no more editing to do on your map.