I currently have 100 US dollars (2009 series) and want to use them anywhere in the world.
They are valid, in the sense that they are legal tender accepted by the US Government, but any individual business anywhere in the world can decide whether or not to accept them or not. There is no guarantee anyone will accept your money. Some businesses may not accept $100 bills at all (in the United States, it's not uncommon for stores to only accept $20 and smaller), and of course, the place you are going must accept US currency in the first place (US currency is, overall, quite popular worldwide, but only local currency is accepted at most businesses in the vast majority of countries). Some countries have local idiosyncratic practices about currency acceptance, such as not accepting creased or worn bills.
However, the 2009/2009A series is the most recent version of the US $100 bill, containing all the modern security features. If an establishment is willing to accept US $100 bills, they're likely to accept yours.
Most countries have their own currency and will not accept US dollars as payment. However, you can find bureau de change or currency exchange shops in most large cities and international airports where you can change your US dollars into the local currency, or if you are in the US, into the currency of the country you are travelling to.
There are some countries that will accept US dollars, but you should find out what currency is used before you travel.
US $100 bills are one of the most heavily forged currencies in the world, see for example http://en.wikipedia.org/wiki/Superdollar
A new $100 bill with extra security features was introduced October 2013, labelled "Series 2009A"; is that what you have?
Also note that currency may be rejected overseas for reasons that seem trivial; I recently had a number of smaller bills rejected for: a tiny mark from a ball point pen, a worn crease, a tiny tear in the margin, and a bit of red ink from an ATM.