You can search for card titles across all boards, including archived cards. Just press the magnifying glass in the top-right corner, enter a search term and press "search".
The search returns:
Number of hits
Board title (below the cards)
You can then press the card (to open it and go to board), or the board title (in order to go to board, but not open the card).
The search is across all boards independent of where you are when you press the search button.
Please note that the search currently does not search card description or inside comments. Only card titles are searched.