I confess; I do it with a couple of websites' help.
I, Rearrangement Servant (Internet Anagram Server)
Sternest Meanings
I think the most famous anagram is this one, crafted by hand by a college student named Cory Calhoun:
"To be or not to be; that is the question, whether 'tis nobler in the mind to suffer the slings and arrows of outrageous fortune." Anagrammed to: "In one of the Bard's best-thought-of tragedies, our insistent hero, Hamlet, queries on two fronts about how life turns rotten."