Google does support link exchanges but is very particular of the exchange that it will support. Google has a policy of not supporting back links which are placed on irrelevant sites. There are many people who just in order to increase the back links to their site place the link on any site without paying any attention to the quality of the content and the website.

If there are links in non relevant sites there is no way that Google will support and rather it will penalize the site.

Google search works on the basis of content and back links. When the phrase searched for appears on more than one site, Google checks for back links and this is how the search results appear. If the back links are from a non relevant site Google does not accept it.

The websites which have a large number of back links from irrelevant sites penalises them and then consider them to be spam. This will lead to the site not appearing in search results. This is the reason one should be very careful while doing any kind of link exchanges on the sit.