Is there any software out there that can automatically for a large number of picture files change the size so that it will fit onto a 768x1024 desktop, keeping the picture as big as possible but not changing the aspect ratio?
IrfanView has a pretty good batch processing setup.
ImageMagick will do the job if you’re on a Unix system.
GraphicConverter on a Mac.
Automator, a built-in part of Mac OS X, will do this (and a whole lot more).
Microsoft’s Picture Resizer Power toy does a good job.
Another vote for GraphicConverter.
Select “Convert and Modify” from the menu, aim the left part of the dialogue at a folder full of (for example) hi-resolution TIFFs, specify a destination folder (or create a new folder), a format (e.g. JPEG)… you can specify file size in KB or MB, file size in pixels by width (length set to proportional based on width) or file size in pixels by length (width set to proportional based on length), as well as resolution (DPI), and you can use IF statements (e.g., if length is greater than width, set length to 1024 pixels, width proportional, ELSE set width to 1024 pixels, length proportional).
And it’s AppleScriptable 
With a bit of twiddling, you can do this in Photoshop.
Picasa. You can do a batch export and resize.