We present algorithms, models and systems based on Eigentaste 2.0, a patented constant-time collaborative filtering algorithm developed by Goldberg et al. Jester 4.0 is an online joke recommender system that uses Eigentaste to recommend jokes to users: we describe the design and implementation of the system and analyze the data collected. Donation Dashboard 1.0 is a new system that recommends non-profit organizations to users in the form of portfolios of donation amounts: we describe this new system and again analyze the data collected. We also present an extension to Eigentaste 2.0 called Eigentaste 5.0, which uses item clustering to increase the adaptability of Eigentaste while maintaing its constant-time nature. We introduce a new framework for recommending weighted portfolios of items using relative ratings as opposed to absolute ratings. Our Eigentaste Security Framework adapts a formal security framework for collaborative filtering, developed by Mobasher et al., to Eigentaste. Finally, we present Opinion Space 1.0, an experimental new system for visualizing opinions and exchanging ideas. Using key elements of Eigentaste, Opinion Space allows users to express their opinions and visualize where they stand relative to a diversity of other viewpoints. We describe the design and implementation of Opinion Space 1.0 and analyze the data collected. Our experience using mathematical tools to utilize and support the wisdom of crowds has highlighted the importance of incorporating these tools into fun and engaging systems. This allows for the collection of a great deal of data that can then be used to improve or enhance the systems and tools. The systems described are all online and have been widely publicized; as of May 2009 we have collected data from over 70,000 users. This master's report concludes with a summary of future work for the algorithms, models and systems presented.