Love her or hate her, Serena is arguably an amazing tennis player. Her serve is arguably the best in the game today, and her 2nd serve is arguably the best ever among women. She keeps her head cool and her ability to deliver a 2nd serve ace is just uncanny when she wants to do it. She is explosive and even injured she can still usually make her opponents squirm.
She is also probably mentally the toughest woman since Steffi Graf to step onto a tennis court. Her ability to tough out matches and come from behind in situations where she should get beaten is amazing. It takes a lot to beat her and unless you stay on course the entire time she will likely make you pay for any lapse, just a few instances of this:
2003 Aussie SF against Clijsters
the already mentioned US Open match against Venus
2009 Aussie QF against Azarenka- least I think it was 09...down a set and 4-0 in the 2nd?
She usually doesn't get rattled by opponents very much, Venus could do it, and so could Henin...but usually the person across the net just has to flat out smoke her from all angles if they are going to win and Serena is playing well.
She does however have 2 major flaws.
1) Her lack of commitment has lead to her being a massive underacheiver. Based on her 2002-2003 form I and a lot of other people thought she was on track to Martina/ Evert numbers at the majors...but since then she has been sidetracked by off the court interests that have hindered her commitment to her fitness, the tour as a whole, and other things. She was almost a non-entity for a lot of 2004-2008 save the 2 Australians she won in that time, and her performance at the 2004 YEC. She rebounded in 2008 though and had a 2nd smaller wave of dominance in the wake of Henin's disappearance.
2) She has iron nerves at times with her opponents, but she certainly has a lot of trouble keeping her cool anytime the officiating goes in anyway against her. No I am not just taking the 2009 and 2011 US Open Fiascos, although those are really enough. She lost her head during the poor officiating at the 2004 US Open QF against Capriati, smacking endless UE's and losing. Now the officiating stunk big time, but Serena did herself no favors by allowing it to bother her to the level it did. The 2003 French Open is also an example, the chairs call rattled her immensely in regards to the hand incident and her form was altered the entire match there after. She has a lot of trouble shacking things off, so to speak.
But, in spite of those things she is an amazing player, 13 majors, easily a top 10 player on any sensible all time list, powerful serve, intensity, hunger. Say what you will about her personality and her attitude...but she makes the WTA interesting. You may not like everything that comes out of her mouth, but without a personality like her on the WTA right now it would even more boring then everyone says it is.
