Is it correct to omit number suffix on dates?

If I have a date written: Saturday 16 December is it correct ?

Or does the grammar oblige me to add the number suffix to 16 making 16th as in: Saturday 16th December ?

It is a matter of house style. Some publications will have the style explicitly set out in a standards document. For example, both the Guardian and Wikipedia standardise on not writing the number suffix in dates.

If you are writing for a magazine/etc. copy what other material in that organ does (or, trust subeditors to shape your words into their house style).

If you are in full control, pick a standard, and stick to it.

If you are writing dialogue, consider writing the exact words the person would say, in full -- so that the reader, or an actor, will say the words you had in mind.

The third of March

This is nothing to do with grammar but rather a matter of typography, and one on which practice varies. I prefer the unadorned date, 16 December, and I think that is what might now be generally found in the UK.