And that's where the camera is at a great disadvantage! The human eye has the ability to detect a single photon of light - when properly dark adapted - and some have estimated a total dynamic range of about 20 stops !!
http://clarkvision.com/imagedetail/eye-resolution.html
So - - if the image has uniform lighting - then the camera can produce a fairly good likeness of what you saw with a single shot.
But what really makes for intriguing photos - are lights and shadows - and that is where working images in Post can be helpful - from boosting the darks and blunting the brights to recompose a more faithful JPG rendition from the captured RAW data - to using Auto-Bracket and a HDR program to produce something more like what you remember seeing.
http://essenceinphotography.com/beginning-your-journey-to-perfect-hdr-photography/processing-a-prefect-hdr-photograph/
Just another aspect of Photography designed to keep us off the streets and hidden in our back-room computer labs :D :D

Nope - - but as some have mentioned - many autobracket for purposes of doing HDR in post (post processing)
http://www.stuckincustoms.com/
and if THAT is your purpose - then - yes - you should be shooting Av (for Canonites) - or constant aperture
When auto-bracketing - if so enabled - the camera will shoot 3, 5, 7 shots automatically with constant ISO and Aperture - varying the shutter speed to obtain different exposures - typically +1-2 eV around the camera's nominally determined exposure.
IF the scene is bright enough - you may do this handheld - but if your shutter speeds get much below 1/60 to 1/30 sec (depending on your image stabilization) - you'd be better off on a Tripod.
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IF you don't CARE about HDR - and just want to pick the best shot of the three - then you can shoot whatever mode you want.
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I don't know if your camera supports auto-bracketing - but it is a nice capability to have.