Regardless of their potential for success [2 3], two new services have attempted to "give credit" for the act of peer reviewing. While not explicity monetary, the idea is to formalize credit for an often thankless task that is a vital part of the academic community.
The first of these services is Publons. Named after the "least publishable unit", Publons allows you to formally publish and cite your peer reviews . While the most prolific reviewers seem to be doing their work purely for within-site prestige, treating peer reviews like published manuscripts is an intriguing idea. Publons is also integrated with select proprietary and open-access publishers, making the service most than merely a self-contained curiosity.
UPDATE (5-19): In keeping with the theme (in an appropriately timely manner), I was mentioned in a new PLoS One feature  as one of many reviewers who kept PLoS One publishing for the year of 2014.
 Social capital can be defined as social benefits derived from one's social network. Units of social capital are often derived from providing public goods, gifting, or the exchange of favors. However, social capital accumulation can also be an indicator of reputation (e.g. the more social capital one holds, the greater their reputation).
For a less-than-idyllic example from an academic context, please see: Graur, D. Payback time for referee refusal. Nature, 505, 483 (2014).
 Hossenfelder, S. Publons. Backreaction blog, April 17 (2015).
 Saunders, N. Academic Karma: a case study in how not to use open data. What You're Doing is Rather Desperate blog, February 19 (2015).
 Van Noorden, R. The Scientist Who Get Credit for Peer Review. Nature News, October 9 (2014).
 PLOS ONE 2014 Reviewer Thank You. PLoS One, 10(2), e0121093 doi:10.1371/journal. pone.0121093 (2015).