It depends upon the strain of E. coli you are using. Most E. coli for example will not grow on sucrose, but a few strains will. Likewise many E. coli will not grow on any of the β-glucoside sugars, although a few strains will. And many lab strains have deletions of specific carbon metabolism operons as well which means those strains can't grow on those sugars.
In addition, although E. coli grows great on D-glucose it will not grow on L-glucose (and I think for most sugars it is enantiospecific but I'm not positive about that).