Different forms of the abbreviations for "identification"?

Both the NOAD and the OED report that ID is an abbreviation for identity, identification.

They weren't carrying any ID.
I lost my ID card.

The term id is used in psychoanalysis, and Id is a variant spelling of Eid.

In some contexts, id could be understood as ID, for example in the phrase the user id used when talking of a CMS.

My gut says "ID", but luckily, so does empirical evidence: Google NGrams Viewer overwhelmingly employs "ID", and Canada's Termium terminological database accepts "ID" as correct (scroll down).

Funny that you don't have the one that I think would make the most sense.

Since it is one word, having a period after the first letter doesn't make any sense.

It is not an acronym, so I would rule out ID.

"id" is actually a completely different word that refers to a part of a psyche and "Id" is how you would write it at the beginning of the sentence.

That rules out all for your suggestions. "Id." is what I prefer. "Id.s" being its plural.

None are intrinsically "incorrect" (whatever that really means), but the most common in everyday writing would be "ID" or "I.D.". Especially in the UK, it's really not common to put full stops in this kind of word/abbreviation in real-life usage-- I almost think this seems to be something of a primary-school-teacherism.

I can't recall seeing "i.d." or "I.d.".

The other variants ("Id" and "id") wouldn't usually be used in normal writing contexts, but are quite common in some computing contexts. For example, a common convention for naming functions/methods is to capitalise the first letter of "words" and treat abbreviations as normal "words". With that plus the convention of starting variable names with small letters, you would end up with things like:

getTokenId()

idOfUser

But obviously these are quite domain-specific uses.