If you define reciprocal links to be the exchange of links between sites who have each carefully reviewed related sites or those potentially helpful to their site's visitors, then such reciprocal links will help your site. They have helped since the SEs started using link analysis, and will as long as link analysis is used to rank web pages.
On the other hand we can define reciprocal links quite differently, for people, having seen that the above form of reciprocal links helps sites, have sought to exploit the power of reciprocal links, and thus decide if contacting 10 sites for link exchange will get me 4 links, then if I contact 100,000 sites I should get just that many more links. It is quite easy to send out tens of thousands of emails per day, or even hundreds of thousands. The problem with this method is that you lose editorial discretion, you lose that individual contact.
If you take the former path (the laborious path) and get a lot of good quality links (from sites that care about who they link to) then your site should perform well, even if the only links you have are recips. If you choose the latter path (the automated spam path) and a get a lot of links from sites that will link to anyone, then those links are not going to count for much.
One of the problems in these forums is that some people, when they refer to reciprocal links, only refer to the latter. Doing reciprocal links properly is hard work and not many people do it right as there are just so many opportunities to slip from the righteous path to the virtueless path.
The chorus here, and at other forums is overwhelmingly that reciprocals don't work and they'll only hurt your site. The SERPs tell a much different story. I can name you dozens of industries that are dominated by sites that use reciprocal linking as their primary form of promotion, where 7 or 8 of the top 10 results will be those powered by recips.