Barcelona has an unusual structure for a tourist city: two or three attractions where booking ahead is genuinely mandatory, and then a large amount of free, self-guided walking that tour companies repackage and sell you.
The mandatory bookings are Sagrada Familia, Park Güell's monumental zone, and whichever Gaudí house you pick. All three are timed entry with hard caps. Sagrada Família in particular has no walk-up option — if you arrive without a ticket you do not get in, full stop.
Where tours are worth it
The Montserrat day trip and the Costa Brava boat day both solve real transport problems and are worth the money. A tapas crawl on your first night is worth it for a different reason: it stops you eating at a Rambla restaurant, which is how most visitors waste their first evening and about sixty euros.
Where they are not
The Gothic Quarter walking tour is the classic example of paying for something free. The quarter is small, dense and full of plaques; a phone and two hours does the same job. Spend the money on the Costa Brava instead.