I am scanning 35mm color slides, some 50 years old, with a Nikon scanner. Should I save the scanned image in jpeg or tiff format for saving on archival CDs?
JPEG is lossy, so the image loses some detail, but the file size may be smaller and compression and extraction can be faster. Wikipedia states, "[It] somewhat reduces the image fidelity... JPEG is also not well suited to files that will undergo multiple edits, as some image quality will usually be lost each time the image is decompressed and recompressed."
TIFF images are larger, but do support lossless ZIP and LZH compression.
If you use or ever plan to use high-end image editing tools (e.g. Adobe Photoshop), TIFF would be preferable. If you're concerned about disk space, JPEG might offer an advantage, though at the expense of image accuracy. JPEG's are also the most convenient form for using on a website or for sharing with friends.
One other option: have the photos scans saved in both formats, or at least in TIFF, and then use any of a number of free (e.g. IrfanView) or commercial utilities to convert to JPEG as you want to share them. It is easy to convert a batch of them. That way you'll always have the maximum-fidelity TIFF to fall back upon.
For archival purposes it makes sense to scan in a lossless format. Depending on what software you are using, you can save NEFs from Nikon Scan, or RAW from VueScan. I prefer that latter, because it saves the actual data coming from the sensor, thus allowing for lossless editing in the future.
JPG: 8 bits per color channel, the data compression dismisses small details in the information provided by the scanner; i.e. the compression is "lossy".
TIF: Possibly 8 but also allows 16 bits per channel - Packbits, ZIP and LZH compressions are lossless.
For archival purposes I'd use TIF 16-bit.
The files may though become huge, especially in comparison to JPGs.
Depending on actual model - a dedicated film-scanner of makes Nikon, Minolta, Plustek, Reflecta / Pacific Imaging come in somewhere in the range 3000 to 5000 dpi.
Note the difference between the SETTING in the software and the ACTUAL result - the latter is the important and what I refer to above.
Even if you scan at a setting of 6400, 7200 or 10000 dpi (which some of the scanners allow) you won't get actual data above 5000 dpi, but rather a notch or two below.
From this follows that pulling up the scan dpi above a certain point (scanner dependent) is just a waste of time and harddisk space.