For serious collectors of antiques, being able to determine whether an item is a genuine antique vs. a reproduction is critical to building a top-notch antiques collection. Some collectors are not particularly concerned whether an item is genuinely "old"; it may be just the style or appearance of the object from a decorating perspective that is important. Each collector must decide for himself what is truly important.
Some items are intentionally made to deceive. One of the earliest lessons I learned when I first started collecting had to do with the purchase of an "antique" cast iron coin bank. I examined the bank and thought the chipped paint and rust gave it the age I expected. A more experienced dealer took a look at it and pointed out that it was a clever reproduction. The underside of the bank's metal base had a cleanly sheared surface, which indicated that a machine had been used to cut the metal. The paint chipping and rust can easily be created by burying a new item in dirt and pouring water over it. After a few days - you have a great "patina" with newly formed chips and rust that make the item appear "old".
Any regular viewer of the "Antiques Roadshow" series on PBS will see numerous instances where a collector brings in what he believes to be a vintage piece, only to be told by the appraiser that he has a reproduction. Fake items cross all lines within antique collecting - from furniture, to art, to pottery, to glass.
A piece of furniture should be thoroughly examined. Check the wood all the way around for any signs of repairs or replacements. Some pieces may be "married" - where a section of one piece of furniture is combined with a section from a different piece of furniture. For dressers and bureaus, check the interior side of drawers to see whether original hardware has been replaced (there may be two sets of holes where the older hardware used to be). Finally, check the finish very carefully. Many valuable pieces can have their worth cut drastically when original paint or finishes have been removed, sanded, and re-finished.
One final tip: if you think the "find" you have made is too inexpensive based on similar items you have seen, you may have a fake or reproduction. Most of the time, if it's too good to be true, it is probably not authentic.