Facebook paid ads are a great alternative, especially if you are targeting a younger audience. Facebook is the number one social network and (almost) the whole world has an account with it. Facebook ads offer lots of targeting options ‐ you can choose age, location, gender, hobbies of the audience to watch your ads. However, do have in mind that with Facebook generally the click through is lower, so don't get discouraged if on Facebook you get fewer clicks on your ads than on other networks ‐ this is pretty normal.
Bing and Yahoo are Google's competitors not only in the area of search engines but also in online ads. Yahoo!/Bing Ads, formerly known as Microsoft AdCenter appeared after the ad networks of Microsoft and Yahoo! joined forces in order to beat Google AdWords. Yahoo!/Bing ads isn't a cheap alternative to AdWords but you should also consider it because it is really good. Basically they offer search advertising (i.e. ads are placed in the search results of Bing search engine) and if you manage to correctly identify your keywords, you can see huge results.
The biggest online marketplace is also a huge ad board. Amazon Product Ads place your ads on product pages. This makes the positioning very targeted because if a user is reading about a product similar to yours, your ads are likely to catch his or her attention. Since Amazon sells everything but space ships, it is a good alternative for almost any niche because chances are there will be numerous products in your niche to publish your ads alongside.
In addition to the big three AdWords alternatives (i.e. Facebook, Yahoo!/Bing ads, and Amazon), there are many smaller ones that still serve millions of impressions a month. One of them is Clicksor. It isn't the cheapest alternative because it has $0.05 cents a click minimum but it is a good one because its conversions are known to be excellent. If clicks are expensive for you, check the other forms of ads offered by Clicksor, such as popunders and interstitials that are CPM or mixed CPM + clicks.
In terms of cost, 7Search is probably the most cost-effective ad network. It has low per click minimums, high conversions (though this depends on the niche) but also high numbers of fraudulent clicks, as some marketers complain. Nevertheless, even with these allegedly high numbers of fraudulent clicks, it is still a very good alternative to Google AdWords.