It's easy to buy a large bead/pendant (I love big, irregular, faceted stones) and string it on an appropriate chain. Try poking through your local bead shop or buying raw materials on eBay or etsy. I've also found that Macy's is a decent source for chunky, fun jewelry, as long as you have a strong sense of what works on you and what is cheap crap that's not worth buying (avoid plastic; look for real stones and strong construction).
Or, you can find tons of inexpensive, handcrafted, readymade statement pieces on etsy. I don't think I'm the only person who's been gravitating away from mass-market jewelry and toward one-of-a-kind pieces, especially when they feature such gorgeous stones, expert construction, cool vintage elements, and amazing prices.
Here are a few of my favorites:
Statement jewelry is fun because it's all about playing with proportion and scale.
A piece of jewelry that's overwhelming on one person will be relatively miniature and insignificant on someone else. Keep this in mind if you're buying a gift for someone (or for yourself).
It is possible to go TOO large, especially if you're young - many style experts say large statement jewelry is best for women over 50, as large pieces sometimes look too gaudy or costume-y on young women. For the most part, though, I think this rule can be bent in today's free-for-all fashion landscape; I tend to believe that a big, beautiful gemstone, bead or pendant is beautiful on nearly anyone, as long as it complements the person and her outfit, rather than overshadowing it. If you're petite and have, for example, delicate collarbones, a chunky piece of jewelry may make you appear all the more petite and delicate - or it may overwhelm you. Get a feel for what makes a statement without going overboard, then go nuts with your favorite colors and gemstones.
Resources: Bitchin' Etsy Jewelry Makers
The following etsy sellers all sell great statement pieces. Many feature vintage elements, because I'm biased toward a vintage look and recycled/found elements.