What are some organizations that gather scientific data given from average people?

Average people don't collect "scientific data." Average people, however, make observation of various phenomena which, when analyzed by professionals, can provide important information.

For example, various marine biologists solicit underwater photographs of animals knowing that, every once in a while, they're going to stumble upon a species they have never seen before. In some cases, this results in the description of a new species.

Many laypersons take part in providing meteorological observations to weather services which, once placed into a particular analytical sequence, provide valuable information.

Ben Franklin described the Gulf Stream as an important oceanographic phenomenon by soliciting observations of water temperature, by location across the North Atlantic, from ships' captains in colonial days.

There's the annual"Christmas Bird Count."

Diving clubs ask divers to participate in counting fishes. Etc., etc., etc.

Such observations do not comprise "scientific data" unless they are collected as part of a designed program that dictates materials and methods for data collection, quality control over the data and the use of the data, and a statistically valid method for evaluating the data. Layperson data is called "anecdotal" data and, as such, needs to be carefully evaluated for validity, and any conclusions based upon anecdotal data need to be stated with appropriate caveats.