The simple answer is jealousy. Both players are immensely talented. This leads to two types of jealousy. The first (and as a never was, i probably fall into this category) are jealous because we will never be even a fraction as skilled as either. The other comes from being jealous that neither plays for your team. No matter what anyone says, if either joined their team, they'd instantly become that fan's favorite player, or at least one of them.
There is also culture. In Ovi's case, he falls victim to being Russian, and in a world where many still remember the Cold War, that hurts him. In Crosby's case, he comes off as really fake to a lot of fans (I myself kind of agree with this perception).
Now, onto the individual things.
Crosby: The whole whiny thing (which he really was early in his career, though he's definitely grown up quite a bit between last season and this). There's also the whole Golden Boy thing (same reason people hate Tom Brady). He seems to get a lot of favoritism in the league, with calls always seeming to go his way. The truth is, he can play as dirty as anyone (not cheating, just hitting the gray area). I personally don't like his lack of personality and his holier than thou attitude at times, and he can sometimes be hypocritical (defending Cooke and then making accusations against Steckle and coming out against head shots only after he got hurt).
Ovechkin: The guy loves the limelight (and why shouldn't he enjoy stardom?), and people don't like that. People forget that hockey is a game, and the guy plays with genuine passion and loves scoring, and a lot of people don't like his celebrations. He's a physical player, and people tend to make a bigger deal out of it because he's in the spotlight. Anything the guy does will be criticized.