Reciprocal links used to be a good way to build links to your site. You would share links with another website on a “links” page or similar. Now, reciprocal links are worth much less due to link spamming. SEO’s would amass large amounts of links quickly by creating link farms, which are hundreds or thousands of webpages controlled by them. The majority of the links would be from “spammy” looking sites that had nothing to do with the target site. Search engines quickly caught on and put far less value on these types of links. This is why you hear “having a handful of quality links is better than having tons of unrelated links”.
SEO’s answered the change by creating “one way reciprocal” links, where they would triangulate links from various sites so they would not appear to all be linked to one another. In other words, site A would link to site B, but instead of site B linking back to site A, site B would link to site C, and site C would link back to site A. They’ve even gone so far as to spread the hosting of these sites far and wide to further hide their footprint, making it a complex scheme.
None of these are good ideas and we never recommend them. The best way to build links to your site is slowly and organically. This is why it takes so long.
Alternatively, it is OK to link to partners, clients and the authoritative sites if the content is related.