The runner accesses cards in archives and there are 3 agendas in it. The corp's identity is the "Argus Security" (whenever the runner steals an agenda, he or she must either take 1 tag or suffer 2 meat damage). How many times the id's ability triggered? One or three?
Argus gets triggered 3 times. From the rulebook (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
Accessing Multiple Cards When accessing multiple cards, the Runner accesses them one at a time in any order he likes.[...]
The Runner must fully resolve his access to a card (steal it, pay to trash it, etc.) before accessing the next card. If the Runner scores an agenda that gives him seven or more points, he immediately wins the game, even if he would otherwise access more cards.
To summarise: runner accesses all cards in archives. Runner must steal all agendas they access. Runner accesses each card separately and fully resolves each access before continuing to the next card, so Argus ID gets triggered on each steal separately.