There are numerous variants of TIFF files (this acronym meaning Tagged Image File Format). The current version is 6.0. According James D. Murray and William VanRyper (Encyclopedia of Graphics File Formats, O'Reilly & Ass., a book I strongly recommand), only versions 4.0, 5.0 and 6.0 had a widely use. There are nevertheless numerous variants, mainly in the colour depth, in the compression scheme, etc.
This means that just knowing you will have to use a Tiff file from a third party can be both a reason to worry and a reason to keep cool. It happens too often that you can't mount a Tiff file in a DTP package and only get a cryptic message saying that this kind of Tiff can't be opened. As a matter of fact, these problems are mainly encountered with files produced with what we have to call entry-level packages (cheap screen capture utilities, old conversion utilities found on dusty servers, crippled demos, quick and dirty tools).
Experience shows that surprises are less frequent with professional graphic packages. If your budget is tight, check that the files your are producing can be opened in the major packages, mainly if you have to go cross-platform.
However, we would like to stress that it is better not to save in a compressed variant when you have to give a file to a customer who will use it on another platform. In the same vein, DTP users should insist on getting uncompressed Tiff files from their graphists. If you want to save storage, save it on your archive media, not on the Zip cartridge or on the CD-ROM you give to your customers.
In several Microsoft packages (mostly Word and PowerPoint), it happens that you get an error message, when you try to insert a Tiff picture, saying that the picture is too big and can't be opened. At first, I thought it was a matter of little/bigendianess (coded at the beginning of the file by the "MM" for the Motorola/Macintosh big-endian or "II" for the Intel/IBM little-endian coding). Well, things are never so simple.
You can check easily: export a Tiff file from Photoshop with both coding schemes and Microsoft packages happily open it. It must be a matter of compression. Anyway, we've found that you could use the shareware Paint Shop Pro to do a batch "conversion" of these files (just taking Tiff as input and Tiff as output, but in a different folder). Thereafter, Microsoft packages can open the files.