If we're talking about the primarily 4chan based internet troll group that routinely gets into fights with people online, then I have a very negative stance.
Several reasons, mainly that I don't believe in their one single policy. 'I do not agree with what you have to say, but I defend to the death your right to say it.' I don't believe in freedom of speech. My personal views on this are very long and convuluted so I won't get into them but this is basically it. And since this is the only tenet Anonymous hold themselves to it means that we are basically incompatible at the base level.
On a more identifiable level I don't think that Anonymous is a force for much good in this world. For every time they manage to find a paedophile or a cat molestor there are dozens of times when they've harassed children into getting naked, or stalked people in real life and left them threatening messages. Anonymous finds out where people live and attacks them both in the digital plane and the real world. In my mind, this makes them bullies, who laughably think themselves noble defenders of freedom etc.
Anyone remember the 'You Done Goofed' girl? It was an image meme featuring a crying girl and a father yelling incompetently at the internet through her webcam. It was set up to look like the stereotypical redneck father vainly shaking his fist at 'them durned kids.' A story of Anonymous, the proud upstanding geeks being able to laugh at the stupid hillbilly who can't beat them up over a wireless connection. Except that it all started when Anonymous make lewd sexual suggestions to an elementary school girl, including asking her to strip, and then started to send her death threats. The girl ended up under police protection while her father made his ultimately useless rant to try desperately to get them to leave his little girl alone.
And that's the thing. Even when they're doing good it's morally questionable, stalking and cyber terrorism that leaves people frightened and confused, and when they'd not doing good, Anonymous is a collection of the biggest jerks and bullies that you could ever meet, and they have more power than you. Basically it's the easiest way to see how human beings really are. Anonymous were bullied in high school (probably) for being geeks and being weak etc, now they have the power and computer know-how to track people down and attack them, and do they use it responsibly? Do they decide that the cycle of torment has to end somewhere, so they'll do the truly noble thing and stand up for those who need it?
No, they attack the weak and the innocent. SO that's why I don't like them.