べき expresses a similar meaning, but is much more forceful—to the point where it is almost an order. While you may hear it in speech it is a considerably hard expression and is more often used in writing.
タバコをやめるべきです。
You should quit smoking.
約束を守るべきだ。
You should keep promises.
足が痛いなら医者に診てもらうべきだと思います。
If your leg hurts I think you should have the doctor take a look at it.
When used with the verb する it is usually abbreviated.
するべき → すべき
留学すべきかどうかについて、親と真剣に相談します。
Seriously discuss with parents whether or not you should study abroad.
Unlike はず no particle is required to modify a noun.
絶対守るべき約束。
A promise you should definitely keep.
べき can also be used to express a likely result, as well.
驚くべき発見。
Surprising discovery.
べき can be changed to the negative by conjugating the auxiliary verb.
車がなくても赤信号の時に、渡るべきではない。
Even if there aren’t any cars you shouldn’t cross the road when the lights are red.
この町の治安が悪いから夜に家を出掛けるべきではない。
This town isn’t safe and so at night you shouldn’t leave the house.
A more literary way of forming the negative is with べきからず.
イギリスでは高速道路で時速７０マイル以上運転すべからず。
In England you should not drive at over 70mph on the motorways.
Incidentally, べし is the archaic form of べき. You may occasionally see it writing, but it is rarely ever used in speech.