-Have a yard sale (not just for handmade items) and give out your business cards to each visitor.
-Call your local radio talk show and think of a way that you can tie your shop into the current topic. Hopefully, they will talk about your shop on the air. It doesn't always work, but free advertising is always worth a try.
-Make a book or portfolio with big, bright pictures of your items. Flip through it while riding the bus or sitting in a waiting room. Make sure that other people can see what you are looking at. Take every opportunity to talk about your shop. I recommend having business cards easily accessible in case you have to go before you've finished talking.
-Wear clothes or carry a bag that advertises Etsy and/or your shop. I love to put pin back buttons on my purse, include a few funny ones to get people's interest, but also include some like the following. (Click on the pictures from some of my favorite Etsy shops to see more information and find out how to purchase these buttons. The third pic is for custom buttons that you can put your shop address on!)
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-Make bookmarks with your shop address, a picture and/or description of what you sell, and a coupon code. (Ads with coupon codes get more results.) Give the bookmarks to your local library or walk around and slip them into random books.
These are only a small amount of unusual ways to advertise. Feel free to comment and add your own ideas and suggestions!