[NoboruWataya]

Yes, the three file formats I have seen used are FIT, TCX and GPX. FIT and TCX are controlled by Garmin but the documentation (and, in the case of TCX, the schema) is publicly available. I'm not sure what licence it is available under.

GPX is described on its website as being an open standard and is very widely used, both for fitness data and other applications. The purpose of GPX is to describe GPS data; by itself it is not as suitable for fitness data as FIT or TCX as things like heart rate and cadence data are not part of the standard. However, GPX can be extended.

From an open web perspective, GPX with standard extensions for other fitness-related data would probably be best, but FIT and TCX are getting ever more popular. For now, the situation is fine because it's fairly easy to convert between them. The risk is that Garmin tries to close off the TCX and FIT standards in the future.