A relationship cannot be termed serious if none of the following things are talked about. A serious relationship will always touch on more concerning the future and lesser concerning the present.
If you don't talk about these with your partner then you better break up;
1. Individual goals and future
A serious relationship must have talks on the future goals. If you don't talk about your future goals and plans then it is better you call it off because it simply shows the relationship is not serious but rather a waste of time.
2. Your stances on marriage
The two of you should express stance in marriage. Do both of you want to get married? Does only one of you want to get married? Or is both of you not interested in getting married? If these questions are never asked in a relationship then it is not really serious.
3. Your views on kids and family planning
Similar to #2. You should discuss matters kids and family planning if you will devote yourself to ensure the relationship ends in a marriage.
4. Direction of your relationship
Of course you have to express your feelings for each other and where you want the relationship to lead you to. You have to discuss where the relationship is going unless you are not that much interested in staying in the relationship for long.
5. Your sexual needs and habits
Sex is a key aspect of a relationship. Ask if sex is important for one of you, both of you or non of you. This will enable you understand your sexual needs and habits as a couple.