Frequent giveaway leaders: Sidney Crosby, Joe Thornton, Andrei Markov...
Players who play a lot and players who pass a lot will have a lot of giveaways as a natural side effect. Players who don't play much and always bounce the puck off the glass won't rack up giveaways, but that doesn't necessarily make them better with puck security; they just don't have the skill to even attempt the sort of play that might result in a giveaway. Not to mention, if you never have the puck, you'll never give it away.
Giveaways, as a stat, would be much more meaningful if compared to, say, pass attempts. Otherwise, guys with a lot of giveaways are probably guys you would take on your team in a heartbeat -- playmakers who have the puck a lot and like to distribute it.
It doesn't help that giveaways are counted differently in different arenas. Montreal used to be one arena where they counted the most, with the end result that Habs defensemen were all among the league leaders... but somehow would give the puck away half as much on the road than they would at home. They would lead the league in giveaways literally because they were Habs. The Montreal scorers gotten a bit better, but Edmonton hasn't: 715 home giveaways versus 257 road? With that amount of discrepancy, you need to correct for arena bias just to have the stat to have the faintest meaning.