ACZoom

New tickets as of 2008.

It costs CAD$7 to buy the OPUS Card. It is a micro-chip based card, and is necessary to buy weekly or monthly passes. It can store multiple single tickets on it also.
The à la carte tickets are paper-based with a magnetic strip. These have no additional cost other than amount of fare.

There are some serious disadvantages with the OPUS card for tourists:
1) Unlike other cities (Boston for example), Montreal is charging a fee to buy the OPUS card.
2) The OPUS card seems to have an expiry date - which is four years. This means that every four years a new card has to be bought. Leaving aside the cost, it seems very wasteful since the card itself should be in good condition and usable for much longer than four years.
3) Unlike many other cities' cards, the OPUS card does not store cash, so it cannot be used for multiple passengers. It should not have been too hard to allow cash on the card too, and deduct the amount of a ticket with each swipe, thus allowing multiple passengers to use one card. New York (on paper ticket, not smart-card) stores cash on card and also provides a bonus when adding cash. A similar concept should have been supported by OPUS.

Unfortunately, for tourists visiting for multiple weeks, there is no choice but to get a OPUS card since the weekly pass (Mon-Sun validity) will not be available in paper-ticket form. Monthly pass is also only available on OPUS.

Another problem for US tourists is that credit cards may not work in the automated machines. While the STM web site claims credit cards are allowed, a bunch of cards I tried were all denied. All I can think of is it had something to do with non-Canada billing address credit cards are not accepted? In any case, try a credit card, but keep cash around when you go to buy a ticket. On the bus, only coins are accepted.

There are some good options for short-time travels, without need the expensive OPUS card.
24-hour travel, 6PM+ travel for that night, are great options. Note that the 3-day consecutive ticket expires midnight on the third day (so it is not a 72-hour pass).

When coming or going to the airport, best to buy the 1-day or 3-day or longer pass. It works on the 747 Express Airport bus. Be careful of buying a ticket for this - there are two versions of the ticket, both cost the case. But one version only allows a single trip on this bus, the other allows travel on metro, bus, for a 24 hour period (i.e., the second one is same as the 1-day pass. This is very confusing, and there are stories of tourists getting the wrong ticket on the bus, so better to ask for a 1-day pass rather than a 747 Bus ticket.

Main web sites:
OPUS Card
À la carte Tickets