What is the ranking of the tallest free standing mountains in the world? I am particularly interested in the ranking of Mount Shasta in North California.

Mt Shasta is the 8th tallest mountain in California (4,316 m).
http://www.scaruffi.com/travel/shasta.html

Looks like it is the 308th highest mountain in the world, but you may want to count them again.
http://www.scaruffi.com/travel/tallest.html"> http://www.scaruffi.com/travel/tallest.html

The tallest free standing mountain (on land) is Nanga Parbat, which ranks as 9th tallest overall from sea level. It rises about 22,000 feet from the Indus river to the summit, in just a few miles.

Exactly what rank Mt. Shasta comes probably depends on the definition of the mountain's base, so I'd be surprised if you get a definite answer.