Barcelona has all the souvenirs you'd find in the rest of Spain (bull-fighting posters, Andalusian pottery, hand-fans etc.). Then there are the souvenirs specific to Barcelona and Catalonia - like miniatures of La Sagrada Familia and Barça football jerseys. If you want to buy cheap throwaway gifts and the usual tourist tack, including Mexican sombreros (nothing to do with Spain whatsoever), flamenco dresses, postcards and mass-produced Sagrada Familia models, Las Ramblas is the ideal spot.
Dig deeper though and you can find unusual gifts which reflect Catalonian culture.
For instance, figurines of the caganer ('the shitter'), a cheeky Catalan peasant always included in any christmas nativity scene (he's the one crouching down with his trousers around his ankles). Scatology is something of a Catalan fixation.
If you're going to get a car sticker, go for a donkey - Catalonia's mascot. Spain's is a bull. Some stickers even have a donkey mounting a bull. Read into that what you will.
In terms of local food and drink, a rosé or white wine from the much-lauded Penedès region of Catalonia is guaranteed to delight. The local version of champagne, cava, is highly-prized and really cheap, on the whole. Take back a bottle of romesco sauce, which is delicious with barbecued spring onions, leaks and vegetables.
Cured meats ('embotits') are a local speciality - particularly morcilla blood sausage and choriço, or a combination of both called 'choriçada', from the Lleida region. These will survive the trip back well too. For sweets, a coca (sweet, crispy pastry) or turró (nougat) might go down well.
Barcelona is home to one of the world's most popular and successful football team, so a replica shirt or leisure wear with the Barça badge is bound to be a winner with kids. At the Camp Nou stadium shop, you can get them printed with the name and number of your choice. Otherwise they're available in any souvenir shop alonng Las Ramblas.
For books in English, including glossy Barcelona architecture and art-related coffee table books, try Happy Books on Portal del Angel. Great Gaudi souvenirs can be purchased in the Gaudi shop right beside the Sagrada Familia on Carrer Mallorca, as well as two souvenir boutiques inside the building (though you'll have to pay to go in).