Three piece suits are not as common as the basic two piece, at least in the States. Find out more about this type and when and where you can get it.
The 3 pieces of this setup include the jacket, trousers, and vest, or waistcoat. They were extremely popular up until the middle part of the 20th century. They were especially popular in colder climates as it gave an extra layer of clothing protection. WWII and cloth shortages made these less and less popular. Today in America, you'll usually only see these on certain bankers, lawyers, or conservative government jobs. They definitely do give out more of a formal air to things.
Note that the acceptable look is to wear suspenders with a three piece, and not a belt. A belt can tend to bunch with the vest and can be uncomfortable. Make sure you have a pair of braces or suspenders if you pick one of these up. Normally the waistcoat is buttoned all the way but its also acceptable to unbutton the bottom button. You can also wear a tie bar to push out the arch of the tie, which some people say looks more sophisticated.
Some people say that they are making somewhat of a comeback in the style scene. Lots of hipsters have taken to wearing waistcoats. Many celebrities love the look including Usher, Johnny Depp, and Brad Pitt.
Many fashion designers have started to come out with new designs, including Armani. They're a little tougher to find in department stores so you may have to dig around a little bit.