Parabens are used as preservatives. You don't want bacteria or mold in your shampoo/conditioner/skin cream, so they're used to prevent that.
This is what I've gathered so far:
They have been used for over 60 years and some sources claim that they're completely safe in small doses. Other claim that some of them can act as estrogens and mess up your hormones. Other say that they can cause cancer, but that seems to be a misunderstanding of a science report that was badly made or something. Most medical sources say that there's no such proof and that it's a internet myth. They can however be irritating to skin and eyes in large doses, like so many other things.
It's very hard to find products that don't include parabens. Some of the common ones are Methylparaben, Propylparaben, Ethylparaben, Buthylparaben. I've read that EU's expert council strongly suggests avoiding Buthylparaben in products for children since it might cause allergies, the other ones are allowed though.
I try to avoid Buthylparaben in products I use, but try not to stress to much about the other ones.
If you search the boards for paraben you'll find lots of threads about this.