Barcelona is now firmly on many Mediterranean cruise ship itineraries, and if you're arriving on one you'll get off at cruise ship terminals A, B, C, or D on the Moll Adossat, in the shadow of Montjuïc, quite far from the historic centre of Barcelona.
The T3 Portbús provides a shuttle service for cruise ship passengers roughly every 20 minutes (depending on when ships arrive) to the Columbus Monument at the base of the Ramblas. There are usually taxis waiting in the rank as well (count on paying around €25 to the airport) or you can arrange a private transfer in advance. If you have a car, park in the Litoral Port car park.
Ferries from the Balearic islands, Rome, Genoa, Sardinia. Tangier etc call in at the Port Vell's more central North and South terminals by the huge bowl-shaped World Trade Center. From here it's a 10 minute walk to the Ramblas.
Image by Kenny Miller