From most visitors, the most common options are:

Single Ride Ticket:  Called a “T+” ticket.  Good for rides on all metro lines and city busses as well as the Montmartre funicular and tramways.  Cost:  1.70 euros.  Purchase a pack of ten, called a “carnet” for 13.30 euros.  Transfers between metro/RER lines are permitted if the rider does not exit the system.  No transfers between bus and metro.

Paris Visite Pass:  A multi-day travel and discount pass heavily marketed to tourists.  Applying my skills from a 30-year career as a mathematics professor, I have yet to find this to be a good value.  Don’t buy it.

Mobilis:  Essentially, it is an all-day unlimited ride T+ ticket.  A one-day pass is 6.60 euro for zones 1-2 (compared to the pricey Paris Visite at 10.55 euro for zones 1-3).  

Navigo Decouverte:  Valid only Monday through Sunday but probably the best value if traveling 4 or more days within this time frame.  It involves purchasing a 5 euro plastic card holder from a ticket agent in which a driver license size photo needs to be attached.  Charge it up at a kiosk for 19.80 euros and ride to your heart’s content on the metro, bus, and RER in the Paris center for a week.

I find I make best use of the unlimited ride passes.  I tend to use public transportation more if I don’t need to ration individual tickets.  

The T+, Mobilis, and Navigo Decouverte fares can be purchased the easy way from a kiosk at nearly every metro station.  Otherwise, deal with a ticket agent speaking limited English through inch-thick bullet-proof ticket-window glass.