Not usually. There are a few formats that have an "encoded by" type field, which may be used to list either software or hardware used for the encoding, but these usually don't necessarily refer to the original capture hardware, more likely the software used to encode the compressed file. I've seen Nikon digital camera video (inside Quicktime container) tagged with the camera model used for capture, but then a similar camera from Canon does not generate similar tags. DSS files do have a field for "hardware", which contains a short model string such as "DS2400" (which you can extrapolate probably refers to the Olympus DS-2400). Digital cameras will usually record the hardware information in still pictures in the EXIF:IFD0 field.
So, in summary:
* most formats: nothing
* few formats: unreliable data
* very few formats: probably-reliable data