Luggages transfer in transit to a different airline

This is almost guaranteed if the two airlines are on the same alliance and likely if the airlines involved have an interline agreement. However, this is at the check-in counter agent's discretion. There are zero guarantees. Be friendly, have your paperwork in order and it'll happen. Have the PNR (six digits and letters) on the connecting flight at hand and make sure it's actually the PNR of the airline not the reservation. The two can differ -- if you can log into the connecting airline with your name and PNR then it's the one you need. If you can't, call the reservation agency beforehand and get the actual PNR(s). In an ordinary situation, you can show up for a flight, present your passport and have the check-in agent sort out the reservation for you but you can't possibly expect that a different airline will bother with this (it's not impossible they can't). For example, I had an Aeroplan award ticket flying on United and Brussels Airlines and there was a (useless) Aeroplan PNR, a United PNR and a Brussels Airlines PNR. When I checked in at ORD it took United more than 15 minutes to sort this mess out (but then again, we know United is incompetent, their own new CEO posted a video essentially saying "we suck"). I bet if I wanted to get my luggage checked through before with another airline they would have refused.

However, there are no guarantees to the opposite either. Delta first announced it won't check through bags effective January 15, 2013 then it postponed this indefinitely and several people on flyertalk, including myself, had no problems with Delta checking through our bags in 2014 at least. Just ask.

This, of course, relates to traditional airlines. Point-to-point low cost airlines will never do this nor will anyone check your baggage through to them. Southwest, Ryanair, whatnot, forget about it. I would say if you can find your airlines among the interline partners of Air Canada then it is very likely you will succeed, if not, then the chances are low. It's not an exhaustive list but it's a very good indicator of "normal" airlines, so to speak.