When are you allowed to use a call sign that is not the aircraft registration? Some General Aviation pilots use their aircraft registration as a call sign, like C-ADYDJ for example. I've heard some use their aircraft type then some numbers like Cessna 45G. Then the typical airliners who use their company name then flight number, like ACA783. 

When are you required to use your aircraft registration, and when are you allowed to replace it? If you are allowed to change it, can anyone use whatever call sign they want or is it limited to airlines only?
For the US, this is covered in AC120-26L, or in a more human-interpretable way from an NBAA article.


  When are you required to use your aircraft registration


By default unless you have a callsign


  Can anyone use whatever call sign they want or is it limited to airlines only?


What you use must be registered. For international flights if you fly frequently enough you can get a 3 letter ICAO designator (SWA, DAL, UAL, etc.)

There are national callsigns which are detailed in that letter, and local callsigns which may apply only to your tower, TRACON, or center depending on who you talk to and what their own rules for issuing a letter of agreement to use it are.