Maxima pumpkins like 'prizewinner', 'bix max' and 'atlantic giant' can have a lot (~800) of very large seeds. But the seed count is variable and sometimes you will get no seeds at all in the pumpkins. Also the large maxima pumpkins take up a lot of space, as much as 2500 square feet.

I know you want to know which pumpkins have the most seeds but there are pumpkins that have been bred for their seeds. They are known as naked seed pumpkins. They don't have the most seeds of any pumpkin, but the seeds are hulless. Some of the varieties include 'Lady Godiva', 'Naked Seed', 'Snackjack' and 'Triple treat'.

In Amy Goldman's book The Compleat Squash, there is a photograph of a group of hull-less seeded pumpkins - 'Kami Kami' is the only one with fiberless tasty flesh (the others being unacceptable for table use) and in the J.L.Hudson catalog it says the Maori (New Zealand) used the immature squash as summer squash as well. I'm trying it myself this year. It's a pretty pumpkin, deeply ribbed with speckled green stripes.