Opened hundreds of years ago in 1470, under the name Mercat Bornet, the legendary Mercat de La Boqueria was once the city's major pig and meat market. The market changed names and identities centuries later, receiving the name Mercat de la Palla, or "straw market"; its modern name (and surrounding walls and roof) didn't arrive until 1840.
Not only is La Boqueria Spain's oldest market, but it has also been granted the title "Best Market in the World," awarded by World Markets Congress, in 2005. And its legacy persists in the vendors who sell there; you'll find second, third, and, in many cases, fourth-generation vendors who have been supplying Barcelona with fresh food for many lifetimes.
The main entrance to La Boqueria is located off La Rambla, Barcelona's main shopping artery. Because of this, the market draws huge crowds of both tourists and locals. Get there early (around 8am) if you want to sit with locals and vendors at Bar Pinotxo. Order a glass of Cava and a café con leche from Juanito Bayen, a Pinotxo mainstay since the early 1980's.
After a glass of Cava, a cup or two of café con leche, and a few tapas, I'd recommend the chipirones with white beans and balsamic glaze—and once you're fueled with those, walk around and take in all the incredible stalls.
Check out snapshots from the market in the slideshow; but if you're taking your own photos, be respectful and ask. Many of the vendors don't appreciate having their photo taken.