Writing out tables from TOPCAT is done using the Save Table Window. In general you have to specify the format in which you want the table to be output by selecting from the Save Window's Table Output Format selector; the following sections describe the possible choices. In some cases there are variants within each format, also described. If you use the default (auto) output format, TOPCAT will try to guess the format based on the filename you provide; the rules for that are described below as well.
The program has no "native" file format, but if you have no particular preference about which format to save tables to, FITS is a good choice. Uncompressed FITS tables do not in most cases have to be read all the way through (they are 'mapped' into memory), which makes them very fast to load up. The FITS format which is written by default (also known as "FITS-plus") also uses a trick to store extra metadata, such as table parameters and UCDs in a way TOPCAT can read in again later (see Section 188.8.131.52). These files are quite usable as normal FITS tables by other applications, but they will only be able to see the limited metadata stored in the FITS headers. For very large files, in some circumstances Column-oriented FITS format format can be more efficient for some applications, though this is unlikely to be understood except by STIL-based code (TOPCAT and STILTS). If you want to write to a format which retains all metadata in a portable format, then one of the VOTable formats might be better.