An example, you have a site on particular gadget and promote products around that gadget. Since all the pages will compose of information around this gadget and there will be products promoted on each page, you are more likely to get sales. Or, can it also work well on sites that are broader nich sites as well?
I think writing reviews about products and comparing them to products that are similar is a good way to get your visitor interested in the product.
It depends on your site. If your site is focused on a certain niche then it is wise to place affiliate programs that match with your site. But there are affiliates that promote various programs in the site.
As Ronald said, if you have a site that talks all about horses, but then decide to use "snake products" as your source of affiliate income, you probably wont find good results. If you have a website based around a certain topic, you want to find affiliate programs that relate.