Project Old Weather, which consists of transcribing pages of the log books of ships which were kept in the 1800-1900s in order to study climate of 150 years ago.
This is needed because computers cannot read the hand-written old log books efficiently (This comes under the umbrella of Zooniverse).
Seti@home, which requires that you just donate your computer time and use the computer to analyse radio signals coming from space and see whether there are repeated patterns.
The Great Sunflower Project, where a member actually has to pay a fee and in return is sent sunflower seeds of a particular species to be planted in the garden. Once the plants grow and flower, they are observed for a specified length of time and the bee visits counted. This is a standardized way to observe the bee population.
The response to the Sunflower project was tremendous: Within six months some 50,000 people signed up.