What determines if a card is placed in the Archives face-up or face-down? I believed it was any card the Runner doesn't know the identity of (i.e. any card not rezzed or accessed), but someone told me yesterday that any card that is trashed must go to the Archives face-up, even if the Runner hadn't yet seen it (example: Noise's ability). Which one is correct?

There's a good thread on this over at Board Game Geek :

http://www.boardgamegeek.com/thread/853186/noise-id-ability-trash-face-down

Here's an excerpt from that thread, that gets to the heart of it :

From page 6 of the rulebook:
Some cards enter Archives faceup, and some cards enter
Archives facedown. Facedown cards in Archives should be
oriented horizontally so that the Runner can easily see them.
Both the Corporation and Runner may look through the
faceup cards stored in Archives at any time, and do not need to
maintain the order of its cards while doing so. The Corporation
can also look at the facedown cards in Archives at any time; the
Runner cannot.

From page 13:
When installing a card in a server, the Corporation can first
trash any cards already installed in that server. Trashed cards go
to Archives faceup if they are rezzed, and facedown if they are
unrezzed.

From page 14: (Doesn't really apply to this question but I'm including this for completeness sake).
Cards discarded from HQ are always sent to Archives
facedown, regardless of whether they have been previously
accessed by the Runner.

From page 18:
Archives: The Runner accesses all cards in Archives and any
upgrades in its root. The Runner turns all cards faceup when
accessing them, and does not need to keep them in order. The
Runner steals all agendas in Archives and cannot trash cards
that are already in Archives. After accessing Archives, all
cards in Archives return to Archives faceup.

So, as you can see from all this, cards trashed by Noise's ability enter the Archives face down in a horizontally oriented pile. (This is because the card in question enters the Archives from an unrezzed state). After the runner makes a successful run on the Archives and accesses all of its cards, all the facedown cards are turned faceup into the vertically oriented pile. This helps the runner keep track of the cards he's seen already.