Matthew, only with limited context would I say 'two over three'.
Perhaps if I was reading it as a mathematics problem, where it's necessary to pronounce your operators, and then only if talking about division, would I use 'two over three'.
"Two over three, plus 5 equals X minus 10." I'd be just as likely to use 'divided by' in place of 'over'.
As any kind of fraction or measurement, it would be 'two-thirds', as others have mentioned above.
For additional reference, here are some other ways to verbalize operators when reading a math problem.
division = over, into
multiplication = times, by
subtraction = from, minus, take away
addition = to, plus, and