The simple answer is, it depends! Each airline, and even sometimes each airport, will have different rules about what is and is not allowed.
As a general rule, most airlines will NOT automatically check your luggage through for an overnight connection. You will normally need collect your luggage when you land, and re-check it the following morning. This is normally a good thing as it allows you access to your luggage for your overnight stay.
However this is not true for all airlines - some WILL check your luggage through, especially for short overnight stays (eg, arrive 11:30pm, depart 5:30am).
The only way to find out exactly what they are going to do is to ask the airline, and even then you might find that when you get to the airport they proceed to do something different anyway!
If you want access to your luggage at the stopover point then basically all airlines will honor such a request at check-in. This is called "short-checking", and although not all airlines will do it in a general sense, they all should for an overnight layover.
If you want them to keep your luggage overnight, then it may be a bit more of a struggle. Some airlines, and even some airports, have policies that they simply will not do this - so whilst you can ask, be ready for a refusal. The one time you may be able to talk them into doing this where they otherwise refuse is if you are not able to go through passport control at the connecting country (eg, you don't have a visa), in which case you will not be able collect your luggage - in this case they may be more willing to check it all the way through, however I would not bet on this always being successful.