Link Exchange - Related Or Non-Related?

Should I exchange links only to those sites which are related or non related? Does it hurt if I exchange links on non related sites?
No it doesn't hurt at all, unless your link is displayed on a non ethical site that would associate your image to that site. That would be bad.
You should also keep in mind that the main goal of link exchange is that users from other sites follow your link. The SEO (search engine optimization) considerations should come after this. In fact, I believe the rules of link exchange are exactly the same as in traditional marketing and common sense should be used.
Targeting your audience
You should try to advertise on sites that are related to yours, or complementary. For instance, exchanging your link with a site that sell vases if you sell flowers, would be a nice idea, because people looking for vases, have high chances to look for flowers too. On the contrary, if you sell flowers, and your link is displayed on a car site, I'm not sure that the interest will be shared, and your link followed.
Quality of links
When you propose to exchange a link with someone, or you participate in a link exchange program, the most probable is that he will put your link in his site but in a place where no one will ever go, with hundreds of other links (and maybe not even linked to the other pages). If that happens, your link will probably never be followed, and be useful only for SEO statistic purposes. You should try to raise the quality of the place where your link is put. Try to exchange first page links to site that are related to your business. Obviously, since you won't be able to place hundred of links on your first page (it is also not recommended to have many links per page), you must choose them well.
SEO considerations (search engine optimization)
With SEO comes the contradiction. It seems that number is more important than quality. If you are using firefox, you will be able to install some SEO addons that even if you don't understand much will show statistics about the site you are visiting. Some of these indicators are related to the number of links identified by main Search Engines. These indicators are valuable to many common users, but if the audience is not properly targeted, they would mean nothing, but for many users it seems to be important to have many links.
Google has also introduced a new parameter. Google robots, when crawling the web to determine what will be the PageRank for your site, will "note" the related links they find, giving a better note to back link than to reciprocal link. In that sense, it would be useful to build a page linked to your mainpage, that proposes to add your image and your link to the visitor's site. To raise your number of backlink, you should also try to participate in forums related to your activity, adding your site URL on your signature. It is also a good way to be known and respected in your area.
Also don't forget that Google is not the only Search Engine. Yahoo (according to Alexa) is still the most visited site. It is good to have a Google friendly site, but only if this doesn't prejudice your appearance on other Search Engines.