Possibly. In your version, Heartgold and Soulsilver (I'm assuming from the tags)...
...in Generations IV and V, when a Pokémon evolves, its personality value is rechecked and the Pokémon's Ability may change.
The previous answer was only partially correct, though. It is luck of the draw, but it is pre-determined. You can't save and reset before evolving it to try for a different ability. Pokemon's abilities are determined by personality value, which, as I said, is pre-determined. I'm not going to go into it, but if you want a different ability on your Tyrogue or Hitmonchan, you'd have to breed for it.
More info on personality value's affect on abilities found here.