First of all, let me introduce myself. I'm Brazilian, and I had the opportunity to follow Neymar's professional career with Santos. I've watched several games of him playing at the Brazileirão (the Brazilian league), the Paulistão (São Paulo's state league), and most recently at the Copa Libertadores (South America's championship; in importance, it's like the Champions League for us). And may I say: if you get him, you'll have a star who is far away from his top game.
First, a brief history about him. Since he was a child, around 13 or 14 years old, he was already treated like a star, and as a saviour for his poor family. He had this huge weight on his back since an early age, and was being spoiled by everyone around him. It translated badly in his 1st and 2nd professional years, as he was, indeed, a locker room cancer and had many trouble on the field with his opponents (doing tricks or trying to score humiliating goals when the game was already closed, falling constantly to force fouls or penalties, arguing with referees), and even with his colleagues on the field (I wish I had the article in English, but last year he refused to get benched after causing some trouble with his opponents, who were almost trying to beat him right there on the field, and when his coach decided to suspend him due to the episode, the coach were fired and Neymar had his suspension canceled).
But it seems like Neymar has matured a lot. He was keen in several games at the Paulistão, scoring many decisive goals or giving many assists when Santos was close to losing or to end up in a draw. The same happened at a bigger stage, in the Copa Libertadores, as he shone again scoring key goals in the last 3 games of the group stage, when Santos was almost out of the competition, and did the same at the final stage. I've seen him taking punches and kicks from whoever was marking him throughout many games, especially at the Copa Libertadores, and still, he managed to at least create 3 or 4 chances for his team to score a goal. Unfortunately, his supporting cast wasn't as good as him, and many of those chances were wasted.
In the end, Neymar succeed to win in a 2 year span 4 of the 5 tournaments he was disputing: 2 Paulistões, 1 Brazilian Cup, and 1 Copa Libertadores.
Now, about the comparisons with Robinho: please, stop it already! They might have the same back-history (both were poor children from the interior of São Paulo, started playing futsal and then professional soccer at Santos, were treated as stars since an early age...), but it stops there. As a player, Neymar is far superior than Robinho.
Robinho has as assets his speed and dribbling. He became famous here in Brazil due to the "pedalada" or step over (video: http://www.youtube.com/watch?v=LBsfnXCvy3g), as he beat many opponents with the move until one of them just crushed his leg and took him out of several games. The problem is, for his position (2nd striker or winger), he should have at least good finishing and composure; two of his serious deficiencies.
It seems like Robinho gets nervous when he has a chance to score. At the Calcio (Italia's soccer league), I've seen him shooting the ball 10 yards away from the goal even when he was at the penalty mark. Also, he seems to have trouble in important matches, and his passing isn't really great. And that's why Neymar and Robinho are different.
Neymar knows what to do with the ball. If he was selfish when he started his pro career, nowadays he's much more willing to give the opportunity to a colleague to score then to try to open up holes in the opponent's defense all by himself. That's why his assists numbers arose, but his goals number kept almost the same. His positioning is great, and his placing shots are a wonderful thing to watch. Also, he has many more dribbling moves than Robinho, and allying that with a good passing ability... damn, why anyone wouldn't want him to play for his team?
But like every normal human being, he has his flaws. Like Messi, he doesn't have a good aerial ability, and he'll have to bulk up to bear the tackling in Europa. He seems to have improved over the years with his ability off the ball, but it's still marginal. His penalty taking is somewhat horrible, but his coaches are working on new techniques for him to improve in this area. Also, it seems like he didn't stop his "acting thing", trying to mislead the referees by falling when the tackle is clean. It hurt him at Copa Libertadores, and even lead him to almost getting suspended for the final game against Peñarol.
Neymar has played in many positions when he was in grassroot soccer at Santos, and did the same at the professional level. He seems to fit better as a winger, either left or right, but I've seen him playing even as a central midfielder here in Brazil. And he can even help in press marking, as he did in some games at the Copa Libertadores when Santos was trying to manage the score.
I haven't read any news recently of him causing any trouble in or off the field. Well, it's true that he had a child with an underage, but he said he is going to offer all the support the child and the mother asks for. That's what you get when you have a different woman every day...
I think the case for Neymar in Barcelona is harder due to his playing style. You guys already have someone who has the ability to open up holes in the opponent's defense even when there are 10 players there to secure the score, and that guy is Messi. And many of the guys who plays for Barça today have been playing together since they were children, and it might be difficult for Neymar to adapt to the locker room (even though he finds the same situation at Santos).
But there's an advantage: the number of Brazilians playing on Barça would help his adaptation. Dani Alves seems to have nurtured a good relationship with him due to the close contact in the Brazil squad, and Neymar reportedly talked to Keirrison about Barça, the city of Barcelona, the country, the continent, the girls...
And to those who think Messi and Neymar would have trouble sharing the spotlights: Messi is too humble, and doesn't want to become a locker room cancer, and Neymar is getting the tutorship to become more humble too.
Anyway: if Barça is really willing to wait until the Club World Cup to sign Neymar, you will get a guy with a lot of room to improve, who is versatile and will create many scoring chances for the team. Also, he won't start sobbing in important games against... I don't know... Real Madrid?