There have been numerous significant productions of Julius Caesar since its initial run at the Globe Theatre in 1599.
Here are three captured on film:
Watch the scene between Brutus and Portia performed by David Bradley and Mary Sefton Darr in
the David Bradley production (1950): it begins at about 1:25.
Watch the scene between Brutus and Portia performed by James Mason and Deborah Kerr in
the Joseph L. Mankiewicz production (1953)
The same encounter performed by Richard Pasco and Virginia McKenna in
the Herbert Wise production (BBC TV, 1979)
is not currently available.
Some more recent stage productions:
RSC Production, Stratford-upon-Avon, 2006
RSC Production, Stratford-upon-Avon, 2009
Long Beach (CA) Shakespeare Company production, 2009
Toneelgroep Amsterdam: Romeinse Tragedies: Barbican International Theatre Events, 2009
Screen and Sound Recordings (compiled by Sarah K. Scott)
British Film Institute: National Film and Television Archive
British Library National Sound Archive Audio Recordings
(See also Bryan N. S. Gooch et al. A Shakespeare Music Catalogue. 5 vols. New York: Oxford University Press, 1991.
Film Productions (from International Movie Database)
Blackton, J. Stuart, and William V. Ranous. Julius Caesar (Silent, UK, 1908)
Benson, Frank R. Julius Caesar (Silent, Portugal, 1911)
Moore, Marshall. Brutus and Cassius (Silent, UK, 1918)
Bower, Dallas. Julius Caesar (Television, UK, 1938)
Simpson, Garry. Julius Caesar (Television, USA; 1949)
Bradley, David. Julius Caesar (USA, 1950)
Brett, Leonard. Julius Caesar (Television, UK, 1951)
Mankiewicz, Joseph L. Julius Caesar (USA, 1953) (see above)
Burge, Stuart. Julius Caesar (Television, UK, 1959)
Eyre, Richard. Julius Caesar (Television, USA, 1960)
Grayson, Godfrey. Honourable Murder (UK, 1960; adaptation of Julius Caesar)
Croft, Michael. Julius Caesar (Television, UK, 1964)
Burge, Stuart. Julius Caesar (UK, 1970)
Wise, Herbert. Julius Caesar (UK, 1979) (Television, BBC-TV) (see above)
Langham, Michael. Julius Caesar (Videorecording, USA, 1979)
Rom, Nam. Gedebe (Malaysia, 2002; adaptation of Julius Caesar)