Yes it is theoretically possible that non-carbon life forms exist. The most commonly proposed basis for an alternative biochemical system is the silicon atom, since silicon has many chemical properties similar to carbon and is in the same periodic table group, the carbon group. Like carbon, silicon can create molecules that are sufficiently large to carry biological information. Have a look at this talk for some interesting information: http://www.forbes.com/sites/bruceupbin/2011/09/08/the-evolution-of-non-carbon-life-forms/
Yep. I’m with Sean on this one. Silicon is the element that is most often mentioned as an alternative.
Also, there may be elements out there that we have not yet discovered that might be suitable as building blocks of life. And, there may be other life forms out there that are not like our definition of a “life form”. But then are they life forms?