I personally think that is is very important to use anonymizers whenever possible for most of the tasks on the Internet. All of your movement and actions are tracked and can be easily traced back to you which is probably something that most users on the Internet are either unaware of or do not like at all if they know that this is the case.
One major problem are P2P networks where anonymity is not that easily achieved. If you do lack the technical background you will face severe difficulties on the road to anonymity. There is however a great solution if you want to be anonymous while downloading and sharing files on Bittorrent.