I am using the lovely Blix template. When I used the Visual editor to insert a graphic to be floated left, it created HTML of the form
<img class=alignleft ...>, which previewed as expected, but didn't honor the alignment in the published posts.
I eventually figured out that I could go back and edit the HTML, changing instances of class=alignleft to class=left, whereupon the published posts behaved as expected.
(And yes, the same applies for class=alignright and class=right.)
As a newcomer, I'm not sure why the visual editor creates HTML that the Blix theme doesn't honor. Nor do I know if other templates share this quirk. Hope this helps.