FAT 12/16: 512
FAT 32: 65,536
Clarifying Information: If you are using long file names then you have to keep in mind that long file names use more than one directory record. Long file name entries span multiple records. A short file name directory record uses a single entry.
Also, using lower case letters in a file name will result in a long file name entry regardless of the length of the file name.
Mixing of lower and upper case letters in the file names will also result in long file name directory entries being used.