1.) They must have the ball in their hands. These are players who generally useless on offense without the ball. They are not good spot-up shooters. They aren't going to move well without the ball to get open or get teammates open. They generally look lost in a half-court offense if the ball is not in their hands at all times.
2.) They are not good passers. Now many 0-guards rack up a lot of assists. However that is just because the ball is always in their hands. The only way they pass the ball is if the defense is all over them and teammates are wide open, hence the assists. However, they don't always do this very effectively. For example, in his best years Arenas averaged 6 assists/game, but also 3.5 turnovers/game while averaging 21 shots/game and 10 free throw attempts/game. Last year, Dwayne Wade averaged 7.5 assists/game, but that came with 5 turnovers/game, while taking 22 shots and 10 free throws per game.
3.) They can get their shot -- easily. This kind of goes without saying. All of these guys are effective at creating for themselves/getting open off the dribble, around screens, etc. If they couldn't do this, they would not be playing at all. Often they are spectacularly good at this -- Dwayne Wade for example.
These are the three obvious 0-guard characteristics. However, there are some other more subtle shared characteristics.
4.) They are poor rebounders. These guys want to get out in transition, so they do not hit the defensive glass and they make no attempts to box out anyone.
5.) They are defensive liabilities. Sort of a continuation from #4. All of their energy goes into scoring, not much is left for defense. Now some guys may average a lot of steals, but that is a notoriously misleading statistic when it comes to defense.
6.) Point guard size. Maybe this helps to explain #5 and #4, but these guys generally don't have the size to match up against shooting guards. This does not necessarily imply being short -- Wade is 6-4 and Evans is 6-6.
Given the above, I don't think Brandon Roy belongs on the list. For his career he has averaged 5 assists but only 2 turnovers per game, while taking 16 shots and 6 free throw attempts per game. That does not sound like a guy who has to have the ball in hand -- or maybe I'm wrong and he's just not a very good 0-guard. I think Simmons put him on the list because Roy demands the ball in his hands at the end of games.
There are some other obvious guys who belong on this list. Starting locally, Monta Ellis is definitely a 0-guard. This year he has averaged 5 assists / 4 turnovers per game, while taking 22 shots and 6 free throw attempts per game. This is definitely Arenas/Wade country. Brandon Jennings is borderline. So is Derrick Rose, but in both cases these guys are young enough to "grow out of it." Rodney Stuckey is a 0-guard, but not a very good one. Jason Terry also qualifies, but he doesn't realize it. He thinks he can spot-up and shoot, but he can't.
Finally, I think Bill Simmons got it wrong when he said that Gilbert Arenas invented the 0-guard position. To me, the quintessential and original 0-guard was Allen Iverson. He had a season (01-02) where he averaged 5.5 assists / 4.0 turnovers to go with 28 shots and 10 free throw attempts per game! Now late in his career, he did become a better passer, but was still more of a 0-guard than a point guard.