I did a quick Google search on the topic, and discovered an old Visa press release that stated that during the peak hour for the year of 2005 (Dec 23rd) Visa processed an average of 6,363 transactions per second, or just shy of 3.82 million transactions within a ten minute span.  The same press release made the claim that Visa processed more transactions within a coffee break than all of the world's public stock exchanges have ever done on their best day. combined.  I'm afraid I can't link it however, you will have to search for it yourself.  "How many transactions?" should work.

I could not find any numbers for Paypal, however.