An Anagram, as you know, is a word or phrase made by 
transposing or rearranging the letters of another word 
or phrase.

Dormitory		  Dirty Room
Evangelist		  Evil's Agent
Desperation		  A Rope Ends It
The Morse Code		  Here Come Dots
Slot Machines		  Cash Lost in 'em
Animosity		  Is No Amity
Mother-in-law		  Woman Hitler
Snooze Alarms		  Alas! No More Z's
Alec Guinness		  Genuine Class
Semolina		  Is No Meal
The Public Art Galleries  Large Picture Halls, I Bet
A Decimal Point		  I'm a Dot in Place
The Earthquakes		  That Queer Shake
Eleven plus two		  Twelve plus one
Contradiction		  Accord not in it
Princess Diana		  Ascend in Paris  (freaky, right?)

This one's truly amazing:
"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."

And the Anagram:
"In one of the Bard's best-thought-of tragedies, our 
insistent hero, Hamlet, queries on two fronts about how 
life turns rotten."

And for the grand finale:
"That's one small step for a man, one giant leap for 
mankind."  -  Neil Armstrong

The Anagram:
"Thin man ran; makes a large stride, left planet, pins 
flag on moon! On to Mars!"