We're reading Winter's Tale for class and I just found the scene with the bear. Did they really use a live bear back in Elizabethan times or was it just a man in a suit?
EDIT: This answer was meant as an April Fool's Day prank. There are no records that suggest an actual bear appeared on stage. It is possible, but unlikely. Henry VIII did not have a tame bear named George.
Fantastic question!
Shakespeare's plays are notably light on stage direction. Almost all of the actor's physical cues come from the words being spoken. When you do encounter Shakespearean stage directions, they are usually very short and simple. "Music plays", "they kiss", "she exits", etc. The opening of The Tempest is practically epic in Shakespearean terms:
A tempestuous noise of thunder and lightning heard; Enter a shipmaster and a boatswain.
But you, my friend, just stumbled upon the strangest and most infamous piece of stage direction in the whole canon:
ANTIGONUS:
... A savage clamour!
Well may I get aboard. This is the chase.
I am gone forever!
Exit, pursued by a bear.
Antigonus, as he himself predicts, never returns and is killed by the bear. This scene is almost never performed today with an actual bear. Theater companies have been very creative in the past few centuries at representing the bear as everything from a man in a costume to a dancer with a ribbon of brown fabric to simply projecting the text "Exit, pursued by a bear." on a screen.
For an audience in London during Shakespeare's career (~1585 - 1614), the sight of animals in theaters for entertainment was not uncommon. The ground level of The Globe Theater itself was used as a pit for bear baiting and cock fighting during the breaks between acts. Shakespeare references The Globe's use for chicken fighting in Henry V :
But pardon, and gentles all,
The flat unraised spirits that have dared
On this unworthy scaffold to bring forth
So great an object: can this cockpit hold
The vasty fields of France?
Unlike chickens, bears had entertainment value beyond bloodsport. Street performances in London had featured trained, dancing bears for centuries. William Sommers, Court Jester of King Henry VIII, had a trained bear named George (after the patron saint of England) who was supposedly so well trained that he would drag a cart of food around the table to serve guests at meal times.
So the answer to your question is yes. Shakespeare would have used a live bear on stage in the original production of The Winter's Tale. However, for numerous safety and ethical reasons, you are unlikely to ever see such a spectacle today.
All citations are from the Arden Shakespeare Complete Works.