to introduce a possibility or presumption

I should be surprised if he wrote

to introduce a fact that is the object of comment

It's odd that you should mention that

to express obligation or recommendation

You should take a bus to Marble Arch

in reported speech to express an action or state in the future

She banged on the door and said we should be late

to express probability or expectation

They should be here by noon

to express a polite form of direct statement

I should have thought it was colder than that