Barcelona Bus Turístic links all of the Barcelona tourist sites you could possibly want to visit. It has three routes (map provided as you board), including a northbound and a southbound line which leave from opposite sides of the Plaça de Catalunya. Each takes 1-2 hours.
The hop-on/hop-off format lets you get-off risk-free at any interesting stop, see what interests you, then get back on any later bus at that or any other stop.
One approach is stay on for an entire route, then continue while getting off at locations that interested you earlier. Buses are double-decked, with the upper deck offering much better views...sunscreen essential in summer months, jackets in winter/early spring/late fall. As you first get on, you are offered earphones.
Outlets near every seat let you choose among many languages and playback volumes. As you approach each significant location, you receive audio describing it.
You can buy tickets at the bus stops and elsewhere (e.g., better hotels) valid for one day (€20) or two consecutive days (€26).
BY BUS