What's his maximum possible speed? I don't think we're ever given enough information to determine that. But, on one occasion we do we see him trying to get from one place to another as quickly as possible -- when Pippin and Gandalf ride him from Dol Baran (where they camped with the Rohirrim shortly after leaving Isengard) to Minis Tirith.
According to Appendix B ("The Tale of Years"), they leave Dol Baran during the night on March 5, and arrive at Minis Tirith at dawn on the 9th. When they first meet, Gandalf tells Denethor that it was a journey of 150 leagues (517 mi, 833 km). Since they only travel at night, that's 4 nights of riding. So Shadowfax averaged about 129 miles (208 km) per night, or 10.7 miles per hour (17.3 kph) (if they rode for 12 hours per night).
An average, modern, non-Mearas horse can travel about 20-30 miles per day, so that makes Shadowfax about 5 or 6 times faster.
If his top speed is likewise proportional to that of a typical horse, that means Shadowfax can run 150 miles per hour (241 kph) or faster. That seems.. er.. unlikely, so it's probably a combination of speed and endurance.
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