Tequila Gang, Esperanto Filmoj, Telecinco Cinema, Estudios Picasso, and Sententia Entertainment
Or companies, more like it.
There are a ton of producers and production companies who had a hand in the making of Pan's Labyrinth—probably because they knew how awesome it would be. First on our list is Guillermo del Toro…but, seeing as he was not only a producer but also the screenwriter and director, you should check on the Director/Screenwriter section for more.
All you need to know from the production side is that he made his own production company, Tequila Gang (because why not, he's Guillermo del Toro). Bertha Navarro was a part of this elite tequila squad, having worked with del Toro in the past on projects like Chronos and The Devil's Backbone.
The best-known producer on Pan's Labyrinth was Alfonso Cuarón. You might know him for his most recent venture into space, Gravity, but he's also directed Harry Potter and the Prisoner of Azkaban (which is often considered one of the best HP adaptations) as well as dramas like A Little Princess and Y Tu Mamá Tambièn.
Cuarón also founded the production company Esperanto Filmoj which helped produce Pan's Labyrinth. The name comes from Cuarón's support for the international, artificially constructed language known as Esperanto. Nun vi scias. Frida Torresblanco, who was the head of Esperanto, also helped produce the movie.
Telecinco Cinema (and one of its predecessors, Estudios Picasso) also produced Pan's Labyrinth…although it's amazing they found they time between episodes of their twenty season marathon series Hospital Central, a Spanish ER-type drama.
Telecinco Cinema also produced the likes of Che and Cell 211, which Pan's Labyrinth producer Álvaro Augustín was a part of. Augustín is also known for movies like The Impossible and The Orphanage and the mashup mockumentary, The Impossible Orphanage.
Pan's Labyrinth was also produced by Sententia Entertainment, the film division of CafeFX which specializes in the whole gambit of visual effects including costume/makeup and CGI in other domains like music videos and commercials.
Yeah: they're the people to thank for your nightmares about children-gobbling creatures with hand-eyes.