Ah... reciprocal links. This is definitely one of the more polarized topics in the SEO world. Some SEOs will tell you that they are mega black-hat, punishable by instant death in search engines. Others will tell you that they are absolutely fine and encourage them. As with most things, reality lies somewhere between these to points of view.
In the most simple form, a reciprocal link is a link that points to a Website which in turn has a link back. So, if Site A links to Site B and then Site B links back to Site A, the links are called "reciprocal links".
In contrast, if Site A links to Site B and Site B does not link back, then the link is called a "one-way link".
Here's the truth: Only do reciprocal links when the two sites are of high quality and when the link is of value to the Website visitors. If you follow this principle, you shouldn't have any problems.
For example, if you own a Website that sells bicycle equipment, it might make sense for you to link to a bicycle tire manufacturer's Website. Conversely, it might make sense for them to link back to you, if you sell their tires for example. Something like this is absolutely fine and passes the smell test.
However, if your bicycle Website links to a casino or prescription drug Website and they link back, something about this smells fishy and Google would probably look at that very closely. If you have multiple links like this, you are almost certainly in trouble.
Site-to-Site reciprocal links may be fine if the site quality is high and they are in some way related, however one thing you definitely should try to avoid is getting involved in link farms or complex linking schemes. For example, if you own 10 sites and you try to link them altogether in a daisy-chain type of way, or if you have all of them reciprocating links with each other (even if they are related), then Google may think that you are trying to manipulate ranking, and again you could find yourself in deep trouble.
Remember: Only link to high quality sites that are related to yours, especially if the link is going to be reciprocated. And don't get involved with daisy-chain linking or cross-linking sites.