The root directory in FAT16 was limited to 255 files.
The maximum number of files that you can have in a FAT16 partition in total is 65525 files, assuming that you have just one directory that is not the root directory and that each file takes up one cluster in size.
Although 16 bits is equal to 65536, some clusters are needed to define the directory and partition information.
For FAT32, the largest number of files that you can have in a single directory is just under 4,294,967,296; again assuming that you have one single directory and that each file takes up one cluster in size.
Of course having so many files in one single directory is a very silly thing to do, as performance is VERY degraded.
An example of this is the IE5 Temporary Internet Files cache, where the cache is actually 4 separate directories. Since the time taken to look up the directory is reduced by splitting it into 4 parts, performance is increased, particularly when you have thousands of very small files.
FAT32 is not subject to the 255 file limit in the root directory.
Remember that clusters are needed for long file names as well, not just the data in the file. This is why often on a FAT16 partition the root directory will only have a maximum of around 80 files. The remaining 175 or so files have been taken up by the LFN segments.