You need to buy tickets in advance for any of these that you want to see: La Sagrada Familia, Parc Guell (no tickets sold at the park), Casa Mila/La Pedrera, Casa Batllo, Picasso Museum, and possibly the Palau de la Musica Catalana (English tours can sell out). In general, everyone with a ticket for a specific time frame lines up, then people are allowed to enter in groups as earlier visitors leave (or so it appears--I'm guessing the fire marshall insists). Obviously, the first time slot is a choice option, because there's no risk you'll be tied up elsewhere and unable to get there on time, and there will be no waiting for earlier visitors to leave; you may still have to wait a bit to avoid crowding at a bottleneck (thinking of the two Casas here).
At some sights you can pay extra for a sort of wildcard ticket that supposedly allows you just to show up (perhaps on a specific date, I'm not sure) and enter without waiting. I assume that means you go right to the head of the line, but I haven't bought one of those tickets. The plain-vanilla tickets are already quite expensive.
The good news is that many of the popular sights have hours that extend into the evening, which allows you more than 8 sightseeing hours per day if you don't run out of energy.
The Sant Pau modernista site is really lovely (same architect as Palau de la Musica Catalana) and is that rare bird in Barcelona: a place where you can (up till now) walk right up and buy a ticket for immediate entry. There are also many museums in Barcelona that generally do not have entry lines of any significance. But it seems that a large percentage of tourists want to see many if not all the places I listed above. I'd also want to allow time to walk around the Eixample (to see some of the modernista buildings that are not open to the public) and the medieval Barri Gotic.